ring_theory.polynomial.basic ⟷ Mathlib.RingTheory.Polynomial.Basic

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

@@ -5,8 +5,8 @@ Authors: Kenny Lau
 -/
 import Algebra.CharP.Basic
 import Algebra.GeomSum
-import Data.MvPolynomial.CommRing
-import Data.MvPolynomial.Equiv
+import Algebra.MvPolynomial.CommRing
+import Algebra.MvPolynomial.Equiv
 import RingTheory.Polynomial.Content
 import RingTheory.UniqueFactorizationDomain
 

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

@@ -524,7 +524,7 @@ variable {q : R[X]}
 
 #print Polynomial.mem_ker_modByMonic /-
 theorem mem_ker_modByMonic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q).ker ↔ q ∣ p :=
-  LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
+  LinearMap.mem_ker.trans (modByMonic_eq_zero_iff_dvd hq)
 #align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_modByMonic
 -/
 

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

@@ -160,7 +160,7 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
     simp only [Submodule.coe_mk]
     by_cases hp0 : p = 0
     · subst hp0; simp only [coeff_zero, LinearMap.map_zero, Finset.sum_const_zero]
-    rw [mem_degree_lt, degree_eq_nat_degree hp0, WithBot.coe_lt_coe] at hp 
+    rw [mem_degree_lt, degree_eq_nat_degree hp0, WithBot.coe_lt_coe] at hp
     conv_rhs => rw [p.as_sum_range' n hp, ← Fin.sum_univ_eq_sum_range]
   right_inv := by
     intro f; ext i
@@ -213,7 +213,7 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
   simp [frange, Finset.image_subset_iff]
   simp only [← C_1, coeff_C]
   intro n hn
-  simp only [exists_prop, ite_eq_right_iff, Classical.not_forall] at hn 
+  simp only [exists_prop, ite_eq_right_iff, Classical.not_forall] at hn
   simp [hn]
 #align polynomial.frange_one Polynomial.frange_one
 -/
@@ -505,7 +505,7 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T :=
   by
   intro i hi
-  simp only [frange, Set.mem_image, mem_support_iff, Ne.def, Finset.mem_coe, Finset.coe_image] at hi 
+  simp only [frange, Set.mem_image, mem_support_iff, Ne.def, Finset.mem_coe, Finset.coe_image] at hi
   rcases hi with ⟨n, hn, h'n⟩
   rw [← h'n, coeff_of_subring]
   exact Subtype.mem (coeff p n : T)
@@ -752,10 +752,10 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
   obtain ⟨p, hp⟩ := hR.mul_inv_cancel X_ne_zero
   have hp0 : p ≠ 0 := by
     rintro rfl
-    rw [MulZeroClass.mul_zero] at hp 
+    rw [MulZeroClass.mul_zero] at hp
     exact zero_ne_one hp
   have := degree_lt_degree_mul_X hp0
-  rw [← X_mul, congr_arg degree hp, degree_one, Nat.WithBot.lt_zero_iff, degree_eq_bot] at this 
+  rw [← X_mul, congr_arg degree hp, degree_one, Nat.WithBot.lt_zero_iff, degree_eq_bot] at this
   exact hp0 this
 #align ideal.polynomial_not_is_field Ideal.polynomial_not_isField
 -/
@@ -813,8 +813,8 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
       · apply mt h.2; rw [not_or]; exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
       apply P.sum_mem
       rintro ⟨i, j⟩ hij
-      rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij 
-      simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij 
+      rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij
+      simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij
       obtain hi | hj : i < m ∨ j < n :=
         by
         rw [Classical.or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
@@ -891,7 +891,7 @@ theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       hr.2.1 <| by rw [← constant_coeff_C _ r]; exact h.map _, fun a b hd =>
       by
       obtain ⟨s, a', b', rfl, rfl⟩ := exists_finset_rename₂ a b
-      rw [← algebra_map_eq] at hd ;
+      rw [← algebra_map_eq] at hd;
       have : algebraMap R _ r ∣ a' * b' := by
         convert (kill_compl Subtype.coe_injective).toRingHom.map_dvd hd; simpa; simp
       rw [← rename_C (coe : s → σ)]; let f := (rename (coe : s → σ)).toRingHom
@@ -1006,11 +1006,11 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
                 hm2 k
                   ((I.mem_leading_coeff_nth _ _).2
                     ⟨_, hp, hn ▸ Polynomial.degree_le_natDegree, rfl⟩)
-            rw [I.mem_leading_coeff_nth] at this 
+            rw [I.mem_leading_coeff_nth] at this
             rcases this with ⟨q, hq, hdq, hlqp⟩
             have hq0 : q ≠ 0 := by
-              intro H; rw [← Polynomial.leadingCoeff_eq_zero] at H 
-              rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H ; exact hp0 H
+              intro H; rw [← Polynomial.leadingCoeff_eq_zero] at H
+              rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H; exact hp0 H
             have h1 : p.degree = (q * Polynomial.X ^ (k - q.nat_degree)).degree :=
               by
               rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
@@ -1022,13 +1022,13 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
             have h2 : p.leading_coeff = (q * Polynomial.X ^ (k - q.nat_degree)).leadingCoeff := by
               rw [← hlqp, Polynomial.leadingCoeff_mul_X_pow]
             have := Polynomial.degree_sub_lt h1 hp0 h2
-            rw [Polynomial.degree_eq_natDegree hp0] at this 
+            rw [Polynomial.degree_eq_natDegree hp0] at this
             rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.nat_degree))]
             refine' (Ideal.span ↑s).add_mem _ ((Ideal.span ↑s).mul_mem_right _ _)
             · by_cases hpq : p - q * Polynomial.X ^ (k - q.nat_degree) = 0
               · rw [hpq]; exact Ideal.zero_mem _
               refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
-              rwa [Polynomial.degree_eq_natDegree hpq, WithBot.coe_lt_coe, hn] at this 
+              rwa [Polynomial.degree_eq_natDegree hpq, WithBot.coe_lt_coe, hn] at this
             exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
 #align polynomial.is_noetherian_ring Polynomial.isNoetherianRing
 -/
@@ -1131,7 +1131,7 @@ theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X
     calc
       aeval f (p * (q * q')) v = aeval f (q' * (p * q)) v := by rw [← mul_assoc, mul_comm]
       _ = 0 := by rw [aeval_mul, LinearMap.mul_apply, LinearMap.mem_ker.1 hv, LinearMap.map_zero]
-  rw [aeval_mul] at h_eval₂_qpp' h_eval₂_pqq' 
+  rw [aeval_mul] at h_eval₂_qpp' h_eval₂_pqq'
   refine'
     ⟨aeval f (q * q') v, LinearMap.mem_ker.1 h_eval₂_pqq', aeval f (p * p') v,
       LinearMap.mem_ker.1 h_eval₂_qpp', _⟩
@@ -1220,7 +1220,7 @@ instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
         0 :=
       by apply rename_injective _ Subtype.val_injective; simpa using h
     letI := MvPolynomial.noZeroDivisors_of_finite R { x // x ∈ s ∪ t }
-    rw [mul_eq_zero] at this 
+    rw [mul_eq_zero] at this
     cases this <;> [left; right]
     all_goals simpa using congr_arg (rename Subtype.val) this⟩
 

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

@@ -1320,7 +1320,7 @@ instance (priority := 100) uniqueFactorizationMonoid : UniqueFactorizationMonoid
   by
   haveI := Inhabited.default (NormalizationMonoid D)
   haveI := to_normalized_gcd_monoid D
-  exact ufm_of_gcd_of_wfDvdMonoid
+  exact ufm_of_decomposition_of_wfDvdMonoid
 #align polynomial.unique_factorization_monoid Polynomial.uniqueFactorizationMonoid
 -/
 

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

@@ -720,7 +720,20 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
 -/
 theorem Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type _} (s : Finset ι) (f : ι → R[X])
     (I : Ideal R) (n : ι → ℕ) (h : ∀ i ∈ s, ∀ (k), (f i).coeff k ∈ I ^ (n i - k)) (k : ℕ) :
-    (s.Prod f).coeff k ∈ I ^ (s.Sum n - k) := by classical
+    (s.Prod f).coeff k ∈ I ^ (s.Sum n - k) := by
+  classical
+  induction' s using Finset.induction with a s ha hs generalizing k
+  · rw [sum_empty, prod_empty, coeff_one, zero_tsub, pow_zero, Ideal.one_eq_top]
+    exact Submodule.mem_top
+  · rw [sum_insert ha, prod_insert ha, coeff_mul]
+    apply sum_mem
+    rintro ⟨i, j⟩ e
+    obtain rfl : i + j = k := nat.mem_antidiagonal.mp e
+    apply Ideal.pow_le_pow add_tsub_add_le_tsub_add_tsub
+    rw [pow_add]
+    exact
+      Ideal.mul_mem_mul (h _ (finset.mem_insert.mpr <| Or.inl rfl) _)
+        (hs (fun i hi k => h _ (finset.mem_insert.mpr <| Or.inr hi) _) j)
 #align polynomial.coeff_prod_mem_ideal_pow_tsub Polynomial.coeff_prod_mem_ideal_pow_tsub
 -/
 
@@ -792,6 +805,26 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     · intro f g; simp only [mem_map_C_iff]; contrapose!
       rintro ⟨hf, hg⟩
       classical
+      let m := Nat.find hf
+      let n := Nat.find hg
+      refine' ⟨m + n, _⟩
+      rw [coeff_mul, ← Finset.insert_erase ((@Finset.Nat.mem_antidiagonal _ (m, n)).mpr rfl),
+        Finset.sum_insert (Finset.not_mem_erase _ _), (P.add_mem_iff_left _).Not]
+      · apply mt h.2; rw [not_or]; exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
+      apply P.sum_mem
+      rintro ⟨i, j⟩ hij
+      rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij 
+      simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij 
+      obtain hi | hj : i < m ∨ j < n :=
+        by
+        rw [Classical.or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
+        rintro (hmi | rfl)
+        · rw [← not_le]; intro hnj; exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
+        ·
+          simpa only [eq_self_iff_true, not_true, false_or_iff, add_right_inj,
+            not_and_self_iff] using hij
+      · rw [mul_comm]; apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hf hi)
+      · apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hg hj)
 #align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrime
 -/
 
@@ -870,7 +903,19 @@ variable {σ}
 
 #print MvPolynomial.prime_rename_iff /-
 theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
-    Prime (rename (coe : s → σ) p) ↔ Prime p := by classical
+    Prime (rename (coe : s → σ) p) ↔ Prime p := by
+  classical
+  symm
+  let eqv :=
+    (sum_alg_equiv R _ _).symm.trans
+      (rename_equiv R <| (Equiv.sumComm (↥(sᶜ)) s).trans <| Equiv.Set.sumCompl s)
+  rw [← prime_C_iff ↥(sᶜ), eqv.to_mul_equiv.prime_iff]
+  convert Iff.rfl
+  suffices (rename coe).toRingHom = eqv.to_alg_hom.to_ring_hom.comp C by
+    apply RingHom.congr_fun this
+  · apply ring_hom_ext
+    · intro; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
+    · intro; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
 -/
 
@@ -881,7 +926,35 @@ end Prime
 namespace Polynomial
 
 instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R] : WfDvdMonoid R[X]
-    where wellFounded_dvdNotUnit := by classical
+    where wellFounded_dvdNotUnit := by
+    classical
+    refine'
+      RelHomClass.wellFounded
+        (⟨fun p : R[X] => ((if p = 0 then ⊤ else ↑p.degree : WithTop (WithBot ℕ)), p.leadingCoeff),
+            _⟩ :
+          DvdNotUnit →r Prod.Lex (· < ·) DvdNotUnit)
+        (WellFounded.prod_lex (WithTop.instWellFoundedLT <| WithBot.instWellFoundedLT Nat.lt_wfRel)
+          ‹WfDvdMonoid R›.wellFounded_dvdNotUnit)
+    rintro a b ⟨ane0, ⟨c, ⟨not_unit_c, rfl⟩⟩⟩
+    rw [Polynomial.degree_mul, if_neg ane0]
+    split_ifs with hac
+    · rw [hac, Polynomial.leadingCoeff_zero]
+      apply Prod.Lex.left
+      exact lt_of_le_of_ne le_top WithTop.coe_ne_top
+    have cne0 : c ≠ 0 := right_ne_zero_of_mul hac
+    simp only [cne0, ane0, Polynomial.leadingCoeff_mul]
+    by_cases hdeg : c.degree = 0
+    · simp only [hdeg, add_zero]
+      refine' Prod.Lex.right _ ⟨_, ⟨c.leading_coeff, fun unit_c => not_unit_c _, rfl⟩⟩
+      · rwa [Ne, Polynomial.leadingCoeff_eq_zero]
+      rw [Polynomial.isUnit_iff, Polynomial.eq_C_of_degree_eq_zero hdeg]
+      use c.leading_coeff, unit_c
+      rw [Polynomial.leadingCoeff, Polynomial.natDegree_eq_of_degree_eq_some hdeg]
+    · apply Prod.Lex.left
+      rw [Polynomial.degree_eq_natDegree cne0] at *
+      rw [WithTop.coe_lt_coe, Polynomial.degree_eq_natDegree ane0, ← WithBot.coe_add,
+        WithBot.coe_lt_coe]
+      exact lt_add_of_pos_right _ (Nat.pos_of_ne_zero fun h => hdeg (h.symm ▸ WithBot.coe_zero))
 
 end Polynomial
 

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

@@ -720,20 +720,7 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
 -/
 theorem Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type _} (s : Finset ι) (f : ι → R[X])
     (I : Ideal R) (n : ι → ℕ) (h : ∀ i ∈ s, ∀ (k), (f i).coeff k ∈ I ^ (n i - k)) (k : ℕ) :
-    (s.Prod f).coeff k ∈ I ^ (s.Sum n - k) := by
-  classical
-  induction' s using Finset.induction with a s ha hs generalizing k
-  · rw [sum_empty, prod_empty, coeff_one, zero_tsub, pow_zero, Ideal.one_eq_top]
-    exact Submodule.mem_top
-  · rw [sum_insert ha, prod_insert ha, coeff_mul]
-    apply sum_mem
-    rintro ⟨i, j⟩ e
-    obtain rfl : i + j = k := nat.mem_antidiagonal.mp e
-    apply Ideal.pow_le_pow add_tsub_add_le_tsub_add_tsub
-    rw [pow_add]
-    exact
-      Ideal.mul_mem_mul (h _ (finset.mem_insert.mpr <| Or.inl rfl) _)
-        (hs (fun i hi k => h _ (finset.mem_insert.mpr <| Or.inr hi) _) j)
+    (s.Prod f).coeff k ∈ I ^ (s.Sum n - k) := by classical
 #align polynomial.coeff_prod_mem_ideal_pow_tsub Polynomial.coeff_prod_mem_ideal_pow_tsub
 -/
 
@@ -805,26 +792,6 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     · intro f g; simp only [mem_map_C_iff]; contrapose!
       rintro ⟨hf, hg⟩
       classical
-      let m := Nat.find hf
-      let n := Nat.find hg
-      refine' ⟨m + n, _⟩
-      rw [coeff_mul, ← Finset.insert_erase ((@Finset.Nat.mem_antidiagonal _ (m, n)).mpr rfl),
-        Finset.sum_insert (Finset.not_mem_erase _ _), (P.add_mem_iff_left _).Not]
-      · apply mt h.2; rw [not_or]; exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
-      apply P.sum_mem
-      rintro ⟨i, j⟩ hij
-      rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij 
-      simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij 
-      obtain hi | hj : i < m ∨ j < n :=
-        by
-        rw [Classical.or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
-        rintro (hmi | rfl)
-        · rw [← not_le]; intro hnj; exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
-        ·
-          simpa only [eq_self_iff_true, not_true, false_or_iff, add_right_inj,
-            not_and_self_iff] using hij
-      · rw [mul_comm]; apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hf hi)
-      · apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hg hj)
 #align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrime
 -/
 
@@ -903,19 +870,7 @@ variable {σ}
 
 #print MvPolynomial.prime_rename_iff /-
 theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
-    Prime (rename (coe : s → σ) p) ↔ Prime p := by
-  classical
-  symm
-  let eqv :=
-    (sum_alg_equiv R _ _).symm.trans
-      (rename_equiv R <| (Equiv.sumComm (↥(sᶜ)) s).trans <| Equiv.Set.sumCompl s)
-  rw [← prime_C_iff ↥(sᶜ), eqv.to_mul_equiv.prime_iff]
-  convert Iff.rfl
-  suffices (rename coe).toRingHom = eqv.to_alg_hom.to_ring_hom.comp C by
-    apply RingHom.congr_fun this
-  · apply ring_hom_ext
-    · intro; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
-    · intro; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
+    Prime (rename (coe : s → σ) p) ↔ Prime p := by classical
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
 -/
 
@@ -926,35 +881,7 @@ end Prime
 namespace Polynomial
 
 instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R] : WfDvdMonoid R[X]
-    where wellFounded_dvdNotUnit := by
-    classical
-    refine'
-      RelHomClass.wellFounded
-        (⟨fun p : R[X] => ((if p = 0 then ⊤ else ↑p.degree : WithTop (WithBot ℕ)), p.leadingCoeff),
-            _⟩ :
-          DvdNotUnit →r Prod.Lex (· < ·) DvdNotUnit)
-        (WellFounded.prod_lex (WithTop.instWellFoundedLT <| WithBot.instWellFoundedLT Nat.lt_wfRel)
-          ‹WfDvdMonoid R›.wellFounded_dvdNotUnit)
-    rintro a b ⟨ane0, ⟨c, ⟨not_unit_c, rfl⟩⟩⟩
-    rw [Polynomial.degree_mul, if_neg ane0]
-    split_ifs with hac
-    · rw [hac, Polynomial.leadingCoeff_zero]
-      apply Prod.Lex.left
-      exact lt_of_le_of_ne le_top WithTop.coe_ne_top
-    have cne0 : c ≠ 0 := right_ne_zero_of_mul hac
-    simp only [cne0, ane0, Polynomial.leadingCoeff_mul]
-    by_cases hdeg : c.degree = 0
-    · simp only [hdeg, add_zero]
-      refine' Prod.Lex.right _ ⟨_, ⟨c.leading_coeff, fun unit_c => not_unit_c _, rfl⟩⟩
-      · rwa [Ne, Polynomial.leadingCoeff_eq_zero]
-      rw [Polynomial.isUnit_iff, Polynomial.eq_C_of_degree_eq_zero hdeg]
-      use c.leading_coeff, unit_c
-      rw [Polynomial.leadingCoeff, Polynomial.natDegree_eq_of_degree_eq_some hdeg]
-    · apply Prod.Lex.left
-      rw [Polynomial.degree_eq_natDegree cne0] at *
-      rw [WithTop.coe_lt_coe, Polynomial.degree_eq_natDegree ane0, ← WithBot.coe_add,
-        WithBot.coe_lt_coe]
-      exact lt_add_of_pos_right _ (Nat.pos_of_ne_zero fun h => hdeg (h.symm ▸ WithBot.coe_zero))
+    where wellFounded_dvdNotUnit := by classical
 
 end Polynomial
 

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

@@ -817,7 +817,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
       simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij 
       obtain hi | hj : i < m ∨ j < n :=
         by
-        rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
+        rw [Classical.or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
         rintro (hmi | rfl)
         · rw [← not_le]; intro hnj; exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
         ·
@@ -933,7 +933,7 @@ instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R
         (⟨fun p : R[X] => ((if p = 0 then ⊤ else ↑p.degree : WithTop (WithBot ℕ)), p.leadingCoeff),
             _⟩ :
           DvdNotUnit →r Prod.Lex (· < ·) DvdNotUnit)
-        (WellFounded.prod_lex (WithTop.wellFounded_lt <| WithBot.wellFounded_lt Nat.lt_wfRel)
+        (WellFounded.prod_lex (WithTop.instWellFoundedLT <| WithBot.instWellFoundedLT Nat.lt_wfRel)
           ‹WfDvdMonoid R›.wellFounded_dvdNotUnit)
     rintro a b ⟨ane0, ⟨c, ⟨not_unit_c, rfl⟩⟩⟩
     rw [Polynomial.degree_mul, if_neg ane0]

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -213,7 +213,7 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
   simp [frange, Finset.image_subset_iff]
   simp only [← C_1, coeff_C]
   intro n hn
-  simp only [exists_prop, ite_eq_right_iff, not_forall] at hn 
+  simp only [exists_prop, ite_eq_right_iff, Classical.not_forall] at hn 
   simp [hn]
 #align polynomial.frange_one Polynomial.frange_one
 -/
@@ -799,7 +799,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     · intro h; simpa only [coeff_C_zero] using h 0
   · intro h
     constructor
-    · rw [Ne.def, eq_top_iff_one, mem_map_C_iff, not_forall]
+    · rw [Ne.def, eq_top_iff_one, mem_map_C_iff, Classical.not_forall]
       use 0
       rw [coeff_one_zero, ← eq_top_iff_one]; exact h.1
     · intro f g; simp only [mem_map_C_iff]; contrapose!

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

@@ -3,12 +3,12 @@ Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathbin.Algebra.CharP.Basic
-import Mathbin.Algebra.GeomSum
-import Mathbin.Data.MvPolynomial.CommRing
-import Mathbin.Data.MvPolynomial.Equiv
-import Mathbin.RingTheory.Polynomial.Content
-import Mathbin.RingTheory.UniqueFactorizationDomain
+import Algebra.CharP.Basic
+import Algebra.GeomSum
+import Data.MvPolynomial.CommRing
+import Data.MvPolynomial.Equiv
+import RingTheory.Polynomial.Content
+import RingTheory.UniqueFactorizationDomain
 
 #align_import ring_theory.polynomial.basic from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.basic
-! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.CharP.Basic
 import Mathbin.Algebra.GeomSum
@@ -15,6 +10,8 @@ import Mathbin.Data.MvPolynomial.Equiv
 import Mathbin.RingTheory.Polynomial.Content
 import Mathbin.RingTheory.UniqueFactorizationDomain
 
+#align_import ring_theory.polynomial.basic from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Ring-theoretic supplement of data.polynomial.
 

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

@@ -78,10 +78,12 @@ theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degre
 #align polynomial.mem_degree_le Polynomial.mem_degreeLE
 -/
 
+#print Polynomial.degreeLE_mono /-
 @[mono]
 theorem degreeLE_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLE R m ≤ degreeLE R n := fun f hf =>
   mem_degreeLE.2 (le_trans (mem_degreeLE.1 hf) H)
 #align polynomial.degree_le_mono Polynomial.degreeLE_mono
+-/
 
 #print Polynomial.degreeLE_eq_span_X_pow /-
 theorem degreeLE_eq_span_X_pow {n : ℕ} :
@@ -116,10 +118,12 @@ theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n
 #align polynomial.mem_degree_lt Polynomial.mem_degreeLT
 -/
 
+#print Polynomial.degreeLT_mono /-
 @[mono]
 theorem degreeLT_mono {m n : ℕ} (H : m ≤ n) : degreeLT R m ≤ degreeLT R n := fun f hf =>
   mem_degreeLT.2 (lt_of_lt_of_le (mem_degreeLT.1 hf) <| WithBot.coe_le_coe.2 H)
 #align polynomial.degree_lt_mono Polynomial.degreeLT_mono
+-/
 
 #print Polynomial.degreeLT_eq_span_X_pow /-
 theorem degreeLT_eq_span_X_pow {n : ℕ} :
@@ -170,18 +174,22 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
 #align polynomial.degree_lt_equiv Polynomial.degreeLTEquiv
 -/
 
+#print Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero /-
 @[simp]
 theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) :
     degreeLTEquiv _ _ ⟨p, hp⟩ = 0 ↔ p = 0 := by
   rw [LinearEquiv.map_eq_zero_iff, Submodule.mk_eq_zero]
 #align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero
+-/
 
+#print Polynomial.eval_eq_sum_degreeLTEquiv /-
 theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
     p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
   by
   simp_rw [eval_eq_sum]
   exact (sum_fin _ (by simp_rw [MulZeroClass.zero_mul, forall_const]) (mem_degree_lt.mp hp)).symm
 #align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquiv
+-/
 
 #print Polynomial.frange /-
 /-- The finset of nonzero coefficients of a polynomial. -/
@@ -196,9 +204,11 @@ theorem frange_zero : frange (0 : R[X]) = ∅ :=
 #align polynomial.frange_zero Polynomial.frange_zero
 -/
 
+#print Polynomial.mem_frange_iff /-
 theorem mem_frange_iff {p : R[X]} {c : R} : c ∈ p.frange ↔ ∃ n ∈ p.support, c = p.coeff n := by
   simp [frange, eq_comm]
 #align polynomial.mem_frange_iff Polynomial.mem_frange_iff
+-/
 
 #print Polynomial.frange_one /-
 theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
@@ -211,11 +221,13 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
 #align polynomial.frange_one Polynomial.frange_one
 -/
 
+#print Polynomial.coeff_mem_frange /-
 theorem coeff_mem_frange (p : R[X]) (n : ℕ) (h : p.coeff n ≠ 0) : p.coeff n ∈ p.frange :=
   by
   simp only [frange, exists_prop, mem_support_iff, Finset.mem_image, Ne.def]
   exact ⟨n, h, rfl⟩
 #align polynomial.coeff_mem_frange Polynomial.coeff_mem_frange
+-/
 
 #print Polynomial.geom_sum_X_comp_X_add_one_eq_sum /-
 theorem geom_sum_X_comp_X_add_one_eq_sum (n : ℕ) :
@@ -278,6 +290,7 @@ section Ring
 
 variable [Ring R]
 
+#print Polynomial.restriction /-
 /-- Given a polynomial, return the polynomial whose coefficients are in
 the ring closure of the original coefficients. -/
 def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R)) :=
@@ -288,6 +301,7 @@ def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R))
           else Subring.subset_closure (p.coeff_mem_frange _ H)⟩ :
         Subring.closure (↑p.frange : Set R))
 #align polynomial.restriction Polynomial.restriction
+-/
 
 #print Polynomial.coeff_restriction /-
 @[simp]
@@ -319,11 +333,13 @@ theorem support_restriction (p : R[X]) : support (restriction p) = support p :=
 #align polynomial.support_restriction Polynomial.support_restriction
 -/
 
+#print Polynomial.map_restriction /-
 @[simp]
 theorem map_restriction {R : Type u} [CommRing R] (p : R[X]) :
     p.restriction.map (algebraMap _ _) = p :=
   ext fun n => by rw [coeff_map, Algebra.algebraMap_ofSubring_apply, coeff_restriction]
 #align polynomial.map_restriction Polynomial.map_restriction
+-/
 
 #print Polynomial.degree_restriction /-
 @[simp]
@@ -338,6 +354,7 @@ theorem natDegree_restriction {p : R[X]} : (restriction p).natDegree = p.natDegr
 #align polynomial.nat_degree_restriction Polynomial.natDegree_restriction
 -/
 
+#print Polynomial.monic_restriction /-
 @[simp]
 theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
   by
@@ -345,19 +362,25 @@ theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
   rw [← @coeff_restriction _ _ p]
   exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_restriction Polynomial.monic_restriction
+-/
 
+#print Polynomial.restriction_zero /-
 @[simp]
 theorem restriction_zero : restriction (0 : R[X]) = 0 := by
   simp only [restriction, Finset.sum_empty, support_zero]
 #align polynomial.restriction_zero Polynomial.restriction_zero
+-/
 
+#print Polynomial.restriction_one /-
 @[simp]
 theorem restriction_one : restriction (1 : R[X]) = 1 :=
   ext fun i => Subtype.eq <| by rw [coeff_restriction', coeff_one, coeff_one] <;> split_ifs <;> rfl
 #align polynomial.restriction_one Polynomial.restriction_one
+-/
 
 variable [Semiring S] {f : R →+* S} {x : S}
 
+#print Polynomial.eval₂_restriction /-
 theorem eval₂_restriction {p : R[X]} :
     eval₂ f x p =
       eval₂ (f.comp (Subring.subtype (Subring.closure (p.frange : Set R)))) x p.restriction :=
@@ -365,11 +388,13 @@ theorem eval₂_restriction {p : R[X]} :
   simp only [eval₂_eq_sum, Sum, support_restriction, ← @coeff_restriction _ _ p]
   rfl
 #align polynomial.eval₂_restriction Polynomial.eval₂_restriction
+-/
 
 section ToSubring
 
 variable (p : R[X]) (T : Subring R)
 
+#print Polynomial.toSubring /-
 /-- Given a polynomial `p` and a subring `T` that contains the coefficients of `p`,
 return the corresponding polynomial whose coefficients are in `T`. -/
 def toSubring (hp : (↑p.frange : Set R) ⊆ T) : T[X] :=
@@ -378,11 +403,11 @@ def toSubring (hp : (↑p.frange : Set R) ⊆ T) : T[X] :=
       (⟨p.coeff i, if H : p.coeff i = 0 then H.symm ▸ T.zero_mem else hp (p.coeff_mem_frange _ H)⟩ :
         T)
 #align polynomial.to_subring Polynomial.toSubring
+-/
 
 variable (hp : (↑p.frange : Set R) ⊆ T)
 
-include hp
-
+#print Polynomial.coeff_toSubring /-
 @[simp]
 theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n :=
   by
@@ -392,12 +417,16 @@ theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n
   · rw [h]; rfl
   · rfl
 #align polynomial.coeff_to_subring Polynomial.coeff_toSubring
+-/
 
+#print Polynomial.coeff_toSubring' /-
 @[simp]
 theorem coeff_toSubring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
   coeff_toSubring _ _ hp
 #align polynomial.coeff_to_subring' Polynomial.coeff_toSubring'
+-/
 
+#print Polynomial.support_toSubring /-
 @[simp]
 theorem support_toSubring : support (toSubring p T hp) = support p :=
   by
@@ -406,28 +435,36 @@ theorem support_toSubring : support (toSubring p T hp) = support p :=
   conv_rhs => rw [← coeff_to_subring p T hp]
   exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.support_to_subring Polynomial.support_toSubring
+-/
 
+#print Polynomial.degree_toSubring /-
 @[simp]
 theorem degree_toSubring : (toSubring p T hp).degree = p.degree := by simp [degree]
 #align polynomial.degree_to_subring Polynomial.degree_toSubring
+-/
 
+#print Polynomial.natDegree_toSubring /-
 @[simp]
 theorem natDegree_toSubring : (toSubring p T hp).natDegree = p.natDegree := by simp [nat_degree]
 #align polynomial.nat_degree_to_subring Polynomial.natDegree_toSubring
+-/
 
+#print Polynomial.monic_toSubring /-
 @[simp]
 theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
   by
   simp_rw [monic, leading_coeff, nat_degree_to_subring, ← coeff_to_subring p T hp]
   exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_to_subring Polynomial.monic_toSubring
+-/
 
-omit hp
-
+#print Polynomial.toSubring_zero /-
 @[simp]
 theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 := by ext i; simp
 #align polynomial.to_subring_zero Polynomial.toSubring_zero
+-/
 
+#print Polynomial.toSubring_one /-
 @[simp]
 theorem toSubring_one :
     toSubring (1 : R[X]) T
@@ -435,21 +472,27 @@ theorem toSubring_one :
       1 :=
   ext fun i => Subtype.eq <| by rw [coeff_to_subring', coeff_one, coeff_one] <;> split_ifs <;> rfl
 #align polynomial.to_subring_one Polynomial.toSubring_one
+-/
 
+#print Polynomial.map_toSubring /-
 @[simp]
 theorem map_toSubring : (p.toSubring T hp).map (Subring.subtype T) = p := by ext n; simp [coeff_map]
 #align polynomial.map_to_subring Polynomial.map_toSubring
+-/
 
 end ToSubring
 
 variable (T : Subring R)
 
+#print Polynomial.ofSubring /-
 /-- Given a polynomial whose coefficients are in some subring, return
 the corresponding polynomial whose coefficients are in the ambient ring. -/
 def ofSubring (p : T[X]) : R[X] :=
   ∑ i in p.support, monomial i (p.coeff i : R)
 #align polynomial.of_subring Polynomial.ofSubring
+-/
 
+#print Polynomial.coeff_ofSubring /-
 theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff p n : T) :=
   by
   simp only [of_subring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
@@ -458,7 +501,9 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
   rw [h]
   rfl
 #align polynomial.coeff_of_subring Polynomial.coeff_ofSubring
+-/
 
+#print Polynomial.frange_ofSubring /-
 @[simp]
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T :=
   by
@@ -468,6 +513,7 @@ theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T
   rw [← h'n, coeff_of_subring]
   exact Subtype.mem (coeff p n : T)
 #align polynomial.frange_of_subring Polynomial.frange_ofSubring
+-/
 
 end Ring
 
@@ -558,12 +604,15 @@ section CommSemiring
 
 variable [CommSemiring R] [Semiring S]
 
+#print Ideal.polynomial_mem_ideal_of_coeff_mem_ideal /-
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself -/
 theorem polynomial_mem_ideal_of_coeff_mem_ideal (I : Ideal R[X]) (p : R[X])
     (hp : ∀ n : ℕ, p.coeff n ∈ I.comap (C : R →+* R[X])) : p ∈ I :=
   sum_C_mul_X_pow_eq p ▸ Submodule.sum_mem I fun n hn => I.mul_mem_right _ (hp n)
 #align ideal.polynomial_mem_ideal_of_coeff_mem_ideal Ideal.polynomial_mem_ideal_of_coeff_mem_ideal
+-/
 
+#print Ideal.mem_map_C_iff /-
 /-- The push-forward of an ideal `I` of `R` to `R[X]` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
 theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
@@ -590,7 +639,9 @@ theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
     rw [mul_comm]
     exact (I.map C : Ideal R[X]).mul_mem_left _ (mem_map_of_mem _ (hf n))
 #align ideal.mem_map_C_iff Ideal.mem_map_C_iff
+-/
 
+#print Polynomial.ker_mapRingHom /-
 theorem Polynomial.ker_mapRingHom (f : R →+* S) :
     (Polynomial.mapRingHom f).ker = f.ker.map (C : R →+* R[X]) :=
   by
@@ -598,9 +649,11 @@ theorem Polynomial.ker_mapRingHom (f : R →+* S) :
   rw [mem_map_C_iff, RingHom.mem_ker, Polynomial.ext_iff]
   simp_rw [coe_map_ring_hom, coeff_map, coeff_zero, RingHom.mem_ker]
 #align polynomial.ker_map_ring_hom Polynomial.ker_mapRingHom
+-/
 
 variable (I : Ideal R[X])
 
+#print Ideal.mem_leadingCoeffNth /-
 theorem mem_leadingCoeffNth (n : ℕ) (x) :
     x ∈ I.leadingCoeffNth n ↔ ∃ p ∈ I, degree p ≤ n ∧ p.leadingCoeff = x :=
   by
@@ -624,7 +677,9 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
       exact le_rfl
     · rw [Polynomial.leadingCoeff, ← coeff_mul_X_pow p (n - nat_degree p), this]
 #align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNth
+-/
 
+#print Ideal.mem_leadingCoeffNth_zero /-
 theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :=
   (mem_leadingCoeffNth _ _ _).trans
     ⟨fun ⟨p, hpI, hpdeg, hpx⟩ => by
@@ -632,7 +687,9 @@ theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :
         Nat.eq_zero_of_le_zero (nat_degree_le_of_degree_le hpdeg), ← eq_C_of_degree_le_zero hpdeg],
       fun hx => ⟨C x, hx, degree_C_le, leadingCoeff_C x⟩⟩
 #align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zero
+-/
 
+#print Ideal.leadingCoeffNth_mono /-
 theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤ I.leadingCoeffNth n :=
   by
   intro r hr
@@ -644,7 +701,9 @@ theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤
   rw [← WithBot.coe_add, add_tsub_cancel_of_le H]
   exact le_rfl
 #align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_mono
+-/
 
+#print Ideal.mem_leadingCoeff /-
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x :=
   by
   rw [leading_coeff, Submodule.mem_iSup_of_directed]
@@ -656,7 +715,9 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
     ⟨i + j, I.leading_coeff_nth_mono (Nat.le_add_right _ _),
       I.leading_coeff_nth_mono (Nat.le_add_left _ _)⟩
 #align ideal.mem_leading_coeff Ideal.mem_leadingCoeff
+-/
 
+#print Polynomial.coeff_prod_mem_ideal_pow_tsub /-
 /-- If `I` is an ideal, and `pᵢ` is a finite family of polynomials each satisfying
 `∀ k, (pᵢ)ₖ ∈ Iⁿⁱ⁻ᵏ` for some `nᵢ`, then `p = ∏ pᵢ` also satisfies `∀ k, pₖ ∈ Iⁿ⁻ᵏ` with `n = ∑ nᵢ`.
 -/
@@ -677,6 +738,7 @@ theorem Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type _} (s : Finset ι) (
       Ideal.mul_mem_mul (h _ (finset.mem_insert.mpr <| Or.inl rfl) _)
         (hs (fun i hi k => h _ (finset.mem_insert.mpr <| Or.inr hi) _) j)
 #align polynomial.coeff_prod_mem_ideal_pow_tsub Polynomial.coeff_prod_mem_ideal_pow_tsub
+-/
 
 end CommSemiring
 
@@ -701,6 +763,7 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
 #align ideal.polynomial_not_is_field Ideal.polynomial_not_isField
 -/
 
+#print Ideal.eq_zero_of_constant_mem_of_maximal /-
 /-- The only constant in a maximal ideal over a field is `0`. -/
 theorem eq_zero_of_constant_mem_of_maximal (hR : IsField R) (I : Ideal R[X]) [hI : I.IsMaximal]
     (x : R) (hx : C x ∈ I) : x = 0 :=
@@ -710,6 +773,7 @@ theorem eq_zero_of_constant_mem_of_maximal (hR : IsField R) (I : Ideal R[X]) [hI
   convert I.mul_mem_left (C y) hx
   rw [← C.map_mul, hR.mul_comm y x, hy, RingHom.map_one]
 #align ideal.eq_zero_of_constant_mem_of_maximal Ideal.eq_zero_of_constant_mem_of_maximal
+-/
 
 end Ring
 
@@ -717,6 +781,7 @@ section CommRing
 
 variable [CommRing R]
 
+#print Ideal.isPrime_map_C_iff_isPrime /-
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) ↔ IsPrime P :=
@@ -764,12 +829,15 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
       · rw [mul_comm]; apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hf hi)
       · apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hg hj)
 #align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrime
+-/
 
+#print Ideal.isPrime_map_C_of_isPrime /-
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_of_isPrime {P : Ideal R} (H : IsPrime P) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) :=
   (isPrime_map_C_iff_isPrime P).mpr H
 #align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrime
+-/
 
 #print Ideal.is_fg_degreeLE /-
 theorem is_fg_degreeLE [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
@@ -793,6 +861,7 @@ variable (σ) {r : R}
 
 namespace Polynomial
 
+#print Polynomial.prime_C_iff /-
 theorem prime_C_iff : Prime (C r) ↔ Prime r :=
   ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr =>
     by
@@ -802,6 +871,7 @@ theorem prime_C_iff : Prime (C r) ↔ Prime r :=
       rw [Ideal.map_span, Set.image_singleton]
     exacts [fun h => this (C_eq_zero.1 h), this]⟩
 #align polynomial.prime_C_iff Polynomial.prime_C_iff
+-/
 
 end Polynomial
 
@@ -817,6 +887,7 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial
       convert (finSuccEquiv R d).toMulEquiv.symm.prime_iff
       rw [← fin_succ_equiv_comp_C_eq_C]; rfl
 
+#print MvPolynomial.prime_C_iff /-
 theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   ⟨comap_prime C constantCoeff (constantCoeff_C _), fun hr =>
     ⟨fun h => hr.1 <| by rw [← C_inj, h]; simp, fun h =>
@@ -829,9 +900,11 @@ theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       rw [← rename_C (coe : s → σ)]; let f := (rename (coe : s → σ)).toRingHom
       exact (((prime_C_iff_of_fintype s).2 hr).2.2 a' b' this).imp f.map_dvd f.map_dvd⟩⟩
 #align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iff
+-/
 
 variable {σ}
 
+#print MvPolynomial.prime_rename_iff /-
 theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     Prime (rename (coe : s → σ) p) ↔ Prime p := by
   classical
@@ -847,6 +920,7 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     · intro; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
     · intro; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
+-/
 
 end MvPolynomial
 
@@ -966,22 +1040,29 @@ attribute [instance] Polynomial.isNoetherianRing
 
 namespace Polynomial
 
+#print Polynomial.exists_irreducible_of_degree_pos /-
 theorem exists_irreducible_of_degree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.degree) : ∃ g, Irreducible g ∧ g ∣ f :=
   WfDvdMonoid.exists_irreducible_factor (fun huf => ne_of_gt hf <| degree_eq_zero_of_isUnit huf)
     fun hf0 => not_lt_of_lt hf <| hf0.symm ▸ (@degree_zero R _).symm ▸ WithBot.bot_lt_coe _
 #align polynomial.exists_irreducible_of_degree_pos Polynomial.exists_irreducible_of_degree_pos
+-/
 
+#print Polynomial.exists_irreducible_of_natDegree_pos /-
 theorem exists_irreducible_of_natDegree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.natDegree) : ∃ g, Irreducible g ∧ g ∣ f :=
   exists_irreducible_of_degree_pos <| by contrapose! hf; exact nat_degree_le_of_degree_le hf
 #align polynomial.exists_irreducible_of_nat_degree_pos Polynomial.exists_irreducible_of_natDegree_pos
+-/
 
+#print Polynomial.exists_irreducible_of_natDegree_ne_zero /-
 theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDomain R]
     [WfDvdMonoid R] {f : R[X]} (hf : f.natDegree ≠ 0) : ∃ g, Irreducible g ∧ g ∣ f :=
   exists_irreducible_of_natDegree_pos <| Nat.pos_of_ne_zero hf
 #align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zero
+-/
 
+#print Polynomial.linearIndependent_powers_iff_aeval /-
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 :=
   by
@@ -990,7 +1071,9 @@ theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     coeff, of_finsupp_eq_zero]
   exact Iff.rfl
 #align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aeval
+-/
 
+#print Polynomial.disjoint_ker_aeval_of_coprime /-
 theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     Disjoint (aeval f p).ker (aeval f q).ker :=
   by
@@ -1001,7 +1084,9 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
     LinearMap.mem_ker.1 (Submodule.mem_inf.1 hv).2] using
     congr_arg (fun p : R[X] => aeval f p v) hpq'.symm
 #align polynomial.disjoint_ker_aeval_of_coprime Polynomial.disjoint_ker_aeval_of_coprime
+-/
 
+#print Polynomial.sup_aeval_range_eq_top_of_coprime /-
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=
   by
@@ -1016,7 +1101,9 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
   simpa only [mul_comm p p', mul_comm q q', aeval_one, aeval_add] using
     congr_arg (fun p : R[X] => aeval f p v) hpq'
 #align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprime
+-/
 
+#print Polynomial.sup_ker_aeval_le_ker_aeval_mul /-
 theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     (aeval f p).ker ⊔ (aeval f q).ker ≤ (aeval f (p * q)).ker :=
   by
@@ -1028,7 +1115,9 @@ theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     rw [aeval_mul, LinearMap.mul_apply, LinearMap.mem_ker.1 hy, LinearMap.map_zero]
   rw [LinearMap.mem_ker, ← hxy, LinearMap.map_add, h_eval_x, h_eval_y, add_zero]
 #align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mul
+-/
 
+#print Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime /-
 theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X]}
     (hpq : IsCoprime p q) : (aeval f p).ker ⊔ (aeval f q).ker = (aeval f (p * q)).ker :=
   by
@@ -1052,6 +1141,7 @@ theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X
   rw [add_comm, mul_comm p p', mul_comm q q']
   simpa only [map_add, map_mul, aeval_one] using congr_arg (fun p : R[X] => aeval f p v) hpq'
 #align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime
+-/
 
 end Polynomial
 
@@ -1088,6 +1178,7 @@ instance isNoetherianRing [Finite σ] [IsNoetherianRing R] : IsNoetherianRing (M
 #align mv_polynomial.is_noetherian_ring MvPolynomial.isNoetherianRing
 -/
 
+#print MvPolynomial.noZeroDivisors_fin /-
 /-- Auxiliary lemma:
 Multivariate polynomials over an integral domain
 with variables indexed by `fin n` form an integral domain.
@@ -1101,7 +1192,9 @@ theorem noZeroDivisors_fin (R : Type u) [CommSemiring R] [NoZeroDivisors R] :
     haveI := no_zero_divisors_fin n
     (MvPolynomial.finSuccEquiv R n).Injective.NoZeroDivisors _ (map_zero _) (map_mul _)
 #align mv_polynomial.no_zero_divisors_fin MvPolynomial.noZeroDivisors_fin
+-/
 
+#print MvPolynomial.noZeroDivisors_of_finite /-
 /-- Auxiliary definition:
 Multivariate polynomials in finitely many variables over an integral domain form an integral domain.
 This fact is proven by transport of structure from the `mv_polynomial.no_zero_divisors_fin`,
@@ -1114,6 +1207,7 @@ theorem noZeroDivisors_of_finite (R : Type u) (σ : Type v) [CommSemiring R] [Fi
   haveI := no_zero_divisors_fin R (Fintype.card σ)
   exact (rename_equiv R (Fintype.equivFin σ)).Injective.NoZeroDivisors _ (map_zero _) (map_mul _)
 #align mv_polynomial.no_zero_divisors_of_finite MvPolynomial.noZeroDivisors_of_finite
+-/
 
 instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
     NoZeroDivisors (MvPolynomial σ R) :=
@@ -1140,6 +1234,7 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] : IsDomain (MvPoly
   exact AddMonoidAlgebra.nontrivial
   exact MvPolynomial.noZeroDivisors
 
+#print MvPolynomial.map_mvPolynomial_eq_eval₂ /-
 theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :
     ϕ p = MvPolynomial.eval₂ (ϕ.comp MvPolynomial.C) (fun s => ϕ (MvPolynomial.X s)) p :=
@@ -1151,7 +1246,9 @@ theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ :
   ext
   simp only [monomial_eq, ϕ.map_pow, ϕ.map_prod, ϕ.comp_apply, ϕ.map_mul, Finsupp.prod_pow]
 #align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂
+-/
 
+#print MvPolynomial.mem_ideal_of_coeff_mem_ideal /-
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself,
 multivariate version. -/
 theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPolynomial σ R)
@@ -1165,7 +1262,9 @@ theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPoly
   suffices C (coeff m p) ∈ I by exact I.mul_mem_right (monomial m 1) this
   simpa [Ideal.mem_comap] using hcoe m
 #align mv_polynomial.mem_ideal_of_coeff_mem_ideal MvPolynomial.mem_ideal_of_coeff_mem_ideal
+-/
 
+#print MvPolynomial.mem_map_C_iff /-
 /-- The push-forward of an ideal `I` of `R` to `mv_polynomial σ R` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
 theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
@@ -1197,7 +1296,9 @@ theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
     apply Ideal.mem_map_of_mem _
     exact hf m
 #align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_C_iff
+-/
 
+#print MvPolynomial.ker_map /-
 theorem ker_map (f : R →+* S) :
     (map f : MvPolynomial σ R →+* MvPolynomial σ S).ker = f.ker.map (C : R →+* MvPolynomial σ R) :=
   by
@@ -1205,6 +1306,7 @@ theorem ker_map (f : R →+* S) :
   rw [MvPolynomial.mem_map_C_iff, RingHom.mem_ker, MvPolynomial.ext_iff]
   simp_rw [coeff_map, coeff_zero, RingHom.mem_ker]
 #align mv_polynomial.ker_map MvPolynomial.ker_map
+-/
 
 end MvPolynomial
 

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

@@ -1041,12 +1041,10 @@ theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X
       aeval f (q * (p * p')) v = aeval f (p' * (p * q)) v := by
         rw [mul_comm, mul_assoc, mul_comm, mul_assoc, mul_comm q p]
       _ = 0 := by rw [aeval_mul, LinearMap.mul_apply, LinearMap.mem_ker.1 hv, LinearMap.map_zero]
-      
   have h_eval₂_pqq' :=
     calc
       aeval f (p * (q * q')) v = aeval f (q' * (p * q)) v := by rw [← mul_assoc, mul_comm]
       _ = 0 := by rw [aeval_mul, LinearMap.mul_apply, LinearMap.mem_ker.1 hv, LinearMap.map_zero]
-      
   rw [aeval_mul] at h_eval₂_qpp' h_eval₂_pqq' 
   refine'
     ⟨aeval f (q * q') v, LinearMap.mem_ker.1 h_eval₂_pqq', aeval f (p * p') v,

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -664,18 +664,18 @@ theorem Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type _} (s : Finset ι) (
     (I : Ideal R) (n : ι → ℕ) (h : ∀ i ∈ s, ∀ (k), (f i).coeff k ∈ I ^ (n i - k)) (k : ℕ) :
     (s.Prod f).coeff k ∈ I ^ (s.Sum n - k) := by
   classical
-    induction' s using Finset.induction with a s ha hs generalizing k
-    · rw [sum_empty, prod_empty, coeff_one, zero_tsub, pow_zero, Ideal.one_eq_top]
-      exact Submodule.mem_top
-    · rw [sum_insert ha, prod_insert ha, coeff_mul]
-      apply sum_mem
-      rintro ⟨i, j⟩ e
-      obtain rfl : i + j = k := nat.mem_antidiagonal.mp e
-      apply Ideal.pow_le_pow add_tsub_add_le_tsub_add_tsub
-      rw [pow_add]
-      exact
-        Ideal.mul_mem_mul (h _ (finset.mem_insert.mpr <| Or.inl rfl) _)
-          (hs (fun i hi k => h _ (finset.mem_insert.mpr <| Or.inr hi) _) j)
+  induction' s using Finset.induction with a s ha hs generalizing k
+  · rw [sum_empty, prod_empty, coeff_one, zero_tsub, pow_zero, Ideal.one_eq_top]
+    exact Submodule.mem_top
+  · rw [sum_insert ha, prod_insert ha, coeff_mul]
+    apply sum_mem
+    rintro ⟨i, j⟩ e
+    obtain rfl : i + j = k := nat.mem_antidiagonal.mp e
+    apply Ideal.pow_le_pow add_tsub_add_le_tsub_add_tsub
+    rw [pow_add]
+    exact
+      Ideal.mul_mem_mul (h _ (finset.mem_insert.mpr <| Or.inl rfl) _)
+        (hs (fun i hi k => h _ (finset.mem_insert.mpr <| Or.inr hi) _) j)
 #align polynomial.coeff_prod_mem_ideal_pow_tsub Polynomial.coeff_prod_mem_ideal_pow_tsub
 
 end CommSemiring
@@ -743,26 +743,26 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     · intro f g; simp only [mem_map_C_iff]; contrapose!
       rintro ⟨hf, hg⟩
       classical
-        let m := Nat.find hf
-        let n := Nat.find hg
-        refine' ⟨m + n, _⟩
-        rw [coeff_mul, ← Finset.insert_erase ((@Finset.Nat.mem_antidiagonal _ (m, n)).mpr rfl),
-          Finset.sum_insert (Finset.not_mem_erase _ _), (P.add_mem_iff_left _).Not]
-        · apply mt h.2; rw [not_or]; exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
-        apply P.sum_mem
-        rintro ⟨i, j⟩ hij
-        rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij 
-        simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij 
-        obtain hi | hj : i < m ∨ j < n :=
-          by
-          rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
-          rintro (hmi | rfl)
-          · rw [← not_le]; intro hnj; exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
-          ·
-            simpa only [eq_self_iff_true, not_true, false_or_iff, add_right_inj,
-              not_and_self_iff] using hij
-        · rw [mul_comm]; apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hf hi)
-        · apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hg hj)
+      let m := Nat.find hf
+      let n := Nat.find hg
+      refine' ⟨m + n, _⟩
+      rw [coeff_mul, ← Finset.insert_erase ((@Finset.Nat.mem_antidiagonal _ (m, n)).mpr rfl),
+        Finset.sum_insert (Finset.not_mem_erase _ _), (P.add_mem_iff_left _).Not]
+      · apply mt h.2; rw [not_or]; exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
+      apply P.sum_mem
+      rintro ⟨i, j⟩ hij
+      rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij 
+      simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij 
+      obtain hi | hj : i < m ∨ j < n :=
+        by
+        rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
+        rintro (hmi | rfl)
+        · rw [← not_le]; intro hnj; exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
+        ·
+          simpa only [eq_self_iff_true, not_true, false_or_iff, add_right_inj,
+            not_and_self_iff] using hij
+      · rw [mul_comm]; apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hf hi)
+      · apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hg hj)
 #align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrime
 
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
@@ -814,7 +814,7 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial
   · symm; induction' Fintype.card σ with d hd
     · exact (is_empty_alg_equiv R (Fin 0)).toMulEquiv.symm.prime_iff
     · rw [hd, ← Polynomial.prime_C_iff]
-      convert(finSuccEquiv R d).toMulEquiv.symm.prime_iff
+      convert (finSuccEquiv R d).toMulEquiv.symm.prime_iff
       rw [← fin_succ_equiv_comp_C_eq_C]; rfl
 
 theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
@@ -825,7 +825,7 @@ theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       obtain ⟨s, a', b', rfl, rfl⟩ := exists_finset_rename₂ a b
       rw [← algebra_map_eq] at hd ;
       have : algebraMap R _ r ∣ a' * b' := by
-        convert(kill_compl Subtype.coe_injective).toRingHom.map_dvd hd; simpa; simp
+        convert (kill_compl Subtype.coe_injective).toRingHom.map_dvd hd; simpa; simp
       rw [← rename_C (coe : s → σ)]; let f := (rename (coe : s → σ)).toRingHom
       exact (((prime_C_iff_of_fintype s).2 hr).2.2 a' b' this).imp f.map_dvd f.map_dvd⟩⟩
 #align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iff
@@ -835,17 +835,17 @@ variable {σ}
 theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     Prime (rename (coe : s → σ) p) ↔ Prime p := by
   classical
-    symm
-    let eqv :=
-      (sum_alg_equiv R _ _).symm.trans
-        (rename_equiv R <| (Equiv.sumComm (↥(sᶜ)) s).trans <| Equiv.Set.sumCompl s)
-    rw [← prime_C_iff ↥(sᶜ), eqv.to_mul_equiv.prime_iff]
-    convert Iff.rfl
-    suffices (rename coe).toRingHom = eqv.to_alg_hom.to_ring_hom.comp C by
-      apply RingHom.congr_fun this
-    · apply ring_hom_ext
-      · intro; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
-      · intro; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
+  symm
+  let eqv :=
+    (sum_alg_equiv R _ _).symm.trans
+      (rename_equiv R <| (Equiv.sumComm (↥(sᶜ)) s).trans <| Equiv.Set.sumCompl s)
+  rw [← prime_C_iff ↥(sᶜ), eqv.to_mul_equiv.prime_iff]
+  convert Iff.rfl
+  suffices (rename coe).toRingHom = eqv.to_alg_hom.to_ring_hom.comp C by
+    apply RingHom.congr_fun this
+  · apply ring_hom_ext
+    · intro; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
+    · intro; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
 
 end MvPolynomial
@@ -857,33 +857,33 @@ namespace Polynomial
 instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R] : WfDvdMonoid R[X]
     where wellFounded_dvdNotUnit := by
     classical
-      refine'
-        RelHomClass.wellFounded
-          (⟨fun p : R[X] =>
-              ((if p = 0 then ⊤ else ↑p.degree : WithTop (WithBot ℕ)), p.leadingCoeff), _⟩ :
-            DvdNotUnit →r Prod.Lex (· < ·) DvdNotUnit)
-          (WellFounded.prod_lex (WithTop.wellFounded_lt <| WithBot.wellFounded_lt Nat.lt_wfRel)
-            ‹WfDvdMonoid R›.wellFounded_dvdNotUnit)
-      rintro a b ⟨ane0, ⟨c, ⟨not_unit_c, rfl⟩⟩⟩
-      rw [Polynomial.degree_mul, if_neg ane0]
-      split_ifs with hac
-      · rw [hac, Polynomial.leadingCoeff_zero]
-        apply Prod.Lex.left
-        exact lt_of_le_of_ne le_top WithTop.coe_ne_top
-      have cne0 : c ≠ 0 := right_ne_zero_of_mul hac
-      simp only [cne0, ane0, Polynomial.leadingCoeff_mul]
-      by_cases hdeg : c.degree = 0
-      · simp only [hdeg, add_zero]
-        refine' Prod.Lex.right _ ⟨_, ⟨c.leading_coeff, fun unit_c => not_unit_c _, rfl⟩⟩
-        · rwa [Ne, Polynomial.leadingCoeff_eq_zero]
-        rw [Polynomial.isUnit_iff, Polynomial.eq_C_of_degree_eq_zero hdeg]
-        use c.leading_coeff, unit_c
-        rw [Polynomial.leadingCoeff, Polynomial.natDegree_eq_of_degree_eq_some hdeg]
-      · apply Prod.Lex.left
-        rw [Polynomial.degree_eq_natDegree cne0] at *
-        rw [WithTop.coe_lt_coe, Polynomial.degree_eq_natDegree ane0, ← WithBot.coe_add,
-          WithBot.coe_lt_coe]
-        exact lt_add_of_pos_right _ (Nat.pos_of_ne_zero fun h => hdeg (h.symm ▸ WithBot.coe_zero))
+    refine'
+      RelHomClass.wellFounded
+        (⟨fun p : R[X] => ((if p = 0 then ⊤ else ↑p.degree : WithTop (WithBot ℕ)), p.leadingCoeff),
+            _⟩ :
+          DvdNotUnit →r Prod.Lex (· < ·) DvdNotUnit)
+        (WellFounded.prod_lex (WithTop.wellFounded_lt <| WithBot.wellFounded_lt Nat.lt_wfRel)
+          ‹WfDvdMonoid R›.wellFounded_dvdNotUnit)
+    rintro a b ⟨ane0, ⟨c, ⟨not_unit_c, rfl⟩⟩⟩
+    rw [Polynomial.degree_mul, if_neg ane0]
+    split_ifs with hac
+    · rw [hac, Polynomial.leadingCoeff_zero]
+      apply Prod.Lex.left
+      exact lt_of_le_of_ne le_top WithTop.coe_ne_top
+    have cne0 : c ≠ 0 := right_ne_zero_of_mul hac
+    simp only [cne0, ane0, Polynomial.leadingCoeff_mul]
+    by_cases hdeg : c.degree = 0
+    · simp only [hdeg, add_zero]
+      refine' Prod.Lex.right _ ⟨_, ⟨c.leading_coeff, fun unit_c => not_unit_c _, rfl⟩⟩
+      · rwa [Ne, Polynomial.leadingCoeff_eq_zero]
+      rw [Polynomial.isUnit_iff, Polynomial.eq_C_of_degree_eq_zero hdeg]
+      use c.leading_coeff, unit_c
+      rw [Polynomial.leadingCoeff, Polynomial.natDegree_eq_of_degree_eq_some hdeg]
+    · apply Prod.Lex.left
+      rw [Polynomial.degree_eq_natDegree cne0] at *
+      rw [WithTop.coe_lt_coe, Polynomial.degree_eq_natDegree ane0, ← WithBot.coe_add,
+        WithBot.coe_lt_coe]
+      exact lt_add_of_pos_right _ (Nat.pos_of_ne_zero fun h => hdeg (h.symm ▸ WithBot.coe_zero))
 
 end Polynomial
 

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

@@ -159,7 +159,7 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
     simp only [Submodule.coe_mk]
     by_cases hp0 : p = 0
     · subst hp0; simp only [coeff_zero, LinearMap.map_zero, Finset.sum_const_zero]
-    rw [mem_degree_lt, degree_eq_nat_degree hp0, WithBot.coe_lt_coe] at hp
+    rw [mem_degree_lt, degree_eq_nat_degree hp0, WithBot.coe_lt_coe] at hp 
     conv_rhs => rw [p.as_sum_range' n hp, ← Fin.sum_univ_eq_sum_range]
   right_inv := by
     intro f; ext i
@@ -206,7 +206,7 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
   simp [frange, Finset.image_subset_iff]
   simp only [← C_1, coeff_C]
   intro n hn
-  simp only [exists_prop, ite_eq_right_iff, not_forall] at hn
+  simp only [exists_prop, ite_eq_right_iff, not_forall] at hn 
   simp [hn]
 #align polynomial.frange_one Polynomial.frange_one
 -/
@@ -463,7 +463,7 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T :=
   by
   intro i hi
-  simp only [frange, Set.mem_image, mem_support_iff, Ne.def, Finset.mem_coe, Finset.coe_image] at hi
+  simp only [frange, Set.mem_image, mem_support_iff, Ne.def, Finset.mem_coe, Finset.coe_image] at hi 
   rcases hi with ⟨n, hn, h'n⟩
   rw [← h'n, coeff_of_subring]
   exact Subtype.mem (coeff p n : T)
@@ -636,7 +636,7 @@ theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :
 theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤ I.leadingCoeffNth n :=
   by
   intro r hr
-  simp only [SetLike.mem_coe, mem_leading_coeff_nth] at hr⊢
+  simp only [SetLike.mem_coe, mem_leading_coeff_nth] at hr ⊢
   rcases hr with ⟨p, hpI, hpdeg, rfl⟩
   refine' ⟨p * X ^ (n - m), I.mul_mem_right _ hpI, _, leading_coeff_mul_X_pow⟩
   refine' le_trans (degree_mul_le _ _) _
@@ -693,10 +693,10 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
   obtain ⟨p, hp⟩ := hR.mul_inv_cancel X_ne_zero
   have hp0 : p ≠ 0 := by
     rintro rfl
-    rw [MulZeroClass.mul_zero] at hp
+    rw [MulZeroClass.mul_zero] at hp 
     exact zero_ne_one hp
   have := degree_lt_degree_mul_X hp0
-  rw [← X_mul, congr_arg degree hp, degree_one, Nat.WithBot.lt_zero_iff, degree_eq_bot] at this
+  rw [← X_mul, congr_arg degree hp, degree_one, Nat.WithBot.lt_zero_iff, degree_eq_bot] at this 
   exact hp0 this
 #align ideal.polynomial_not_is_field Ideal.polynomial_not_isField
 -/
@@ -751,8 +751,8 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
         · apply mt h.2; rw [not_or]; exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
         apply P.sum_mem
         rintro ⟨i, j⟩ hij
-        rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij
-        simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij
+        rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij 
+        simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij 
         obtain hi | hj : i < m ∨ j < n :=
           by
           rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
@@ -797,10 +797,10 @@ theorem prime_C_iff : Prime (C r) ↔ Prime r :=
   ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr =>
     by
     have := hr.1
-    rw [← Ideal.span_singleton_prime] at hr⊢
+    rw [← Ideal.span_singleton_prime] at hr ⊢
     · convert Ideal.isPrime_map_C_of_isPrime hr using 1
       rw [Ideal.map_span, Set.image_singleton]
-    exacts[fun h => this (C_eq_zero.1 h), this]⟩
+    exacts [fun h => this (C_eq_zero.1 h), this]⟩
 #align polynomial.prime_C_iff Polynomial.prime_C_iff
 
 end Polynomial
@@ -810,7 +810,7 @@ namespace MvPolynomial
 private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   by
   rw [(rename_equiv R (Fintype.equivFin σ)).toMulEquiv.prime_iff]
-  convert_to Prime (C r) ↔ _; · congr ; apply rename_C
+  convert_to Prime (C r) ↔ _; · congr; apply rename_C
   · symm; induction' Fintype.card σ with d hd
     · exact (is_empty_alg_equiv R (Fin 0)).toMulEquiv.symm.prime_iff
     · rw [hd, ← Polynomial.prime_C_iff]
@@ -823,7 +823,7 @@ theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       hr.2.1 <| by rw [← constant_coeff_C _ r]; exact h.map _, fun a b hd =>
       by
       obtain ⟨s, a', b', rfl, rfl⟩ := exists_finset_rename₂ a b
-      rw [← algebra_map_eq] at hd;
+      rw [← algebra_map_eq] at hd ;
       have : algebraMap R _ r ∣ a' * b' := by
         convert(kill_compl Subtype.coe_injective).toRingHom.map_dvd hd; simpa; simp
       rw [← rename_C (coe : s → σ)]; let f := (rename (coe : s → σ)).toRingHom
@@ -844,8 +844,8 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     suffices (rename coe).toRingHom = eqv.to_alg_hom.to_ring_hom.comp C by
       apply RingHom.congr_fun this
     · apply ring_hom_ext
-      · intro ; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
-      · intro ; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
+      · intro; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
+      · intro; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
 
 end MvPolynomial
@@ -935,11 +935,11 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
                 hm2 k
                   ((I.mem_leading_coeff_nth _ _).2
                     ⟨_, hp, hn ▸ Polynomial.degree_le_natDegree, rfl⟩)
-            rw [I.mem_leading_coeff_nth] at this
+            rw [I.mem_leading_coeff_nth] at this 
             rcases this with ⟨q, hq, hdq, hlqp⟩
             have hq0 : q ≠ 0 := by
-              intro H; rw [← Polynomial.leadingCoeff_eq_zero] at H
-              rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H; exact hp0 H
+              intro H; rw [← Polynomial.leadingCoeff_eq_zero] at H 
+              rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H ; exact hp0 H
             have h1 : p.degree = (q * Polynomial.X ^ (k - q.nat_degree)).degree :=
               by
               rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
@@ -951,13 +951,13 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
             have h2 : p.leading_coeff = (q * Polynomial.X ^ (k - q.nat_degree)).leadingCoeff := by
               rw [← hlqp, Polynomial.leadingCoeff_mul_X_pow]
             have := Polynomial.degree_sub_lt h1 hp0 h2
-            rw [Polynomial.degree_eq_natDegree hp0] at this
+            rw [Polynomial.degree_eq_natDegree hp0] at this 
             rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.nat_degree))]
             refine' (Ideal.span ↑s).add_mem _ ((Ideal.span ↑s).mul_mem_right _ _)
             · by_cases hpq : p - q * Polynomial.X ^ (k - q.nat_degree) = 0
               · rw [hpq]; exact Ideal.zero_mem _
               refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
-              rwa [Polynomial.degree_eq_natDegree hpq, WithBot.coe_lt_coe, hn] at this
+              rwa [Polynomial.degree_eq_natDegree hpq, WithBot.coe_lt_coe, hn] at this 
             exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
 #align polynomial.is_noetherian_ring Polynomial.isNoetherianRing
 -/
@@ -1047,7 +1047,7 @@ theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X
       aeval f (p * (q * q')) v = aeval f (q' * (p * q)) v := by rw [← mul_assoc, mul_comm]
       _ = 0 := by rw [aeval_mul, LinearMap.mul_apply, LinearMap.mem_ker.1 hv, LinearMap.map_zero]
       
-  rw [aeval_mul] at h_eval₂_qpp' h_eval₂_pqq'
+  rw [aeval_mul] at h_eval₂_qpp' h_eval₂_pqq' 
   refine'
     ⟨aeval f (q * q') v, LinearMap.mem_ker.1 h_eval₂_pqq', aeval f (p * p') v,
       LinearMap.mem_ker.1 h_eval₂_qpp', _⟩
@@ -1131,8 +1131,8 @@ instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
         0 :=
       by apply rename_injective _ Subtype.val_injective; simpa using h
     letI := MvPolynomial.noZeroDivisors_of_finite R { x // x ∈ s ∪ t }
-    rw [mul_eq_zero] at this
-    cases this <;> [left;right]
+    rw [mul_eq_zero] at this 
+    cases this <;> [left; right]
     all_goals simpa using congr_arg (rename Subtype.val) this⟩
 
 /-- The multivariate polynomial ring over an integral domain is an integral domain. -/

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

@@ -832,7 +832,6 @@ theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
 
 variable {σ}
 
-#print MvPolynomial.prime_rename_iff /-
 theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     Prime (rename (coe : s → σ) p) ↔ Prime p := by
   classical
@@ -848,7 +847,6 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
       · intro ; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
       · intro ; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
--/
 
 end MvPolynomial
 
@@ -993,7 +991,6 @@ theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
   exact Iff.rfl
 #align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aeval
 
-#print Polynomial.disjoint_ker_aeval_of_coprime /-
 theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     Disjoint (aeval f p).ker (aeval f q).ker :=
   by
@@ -1004,7 +1001,6 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
     LinearMap.mem_ker.1 (Submodule.mem_inf.1 hv).2] using
     congr_arg (fun p : R[X] => aeval f p v) hpq'.symm
 #align polynomial.disjoint_ker_aeval_of_coprime Polynomial.disjoint_ker_aeval_of_coprime
--/
 
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=

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

@@ -36,7 +36,7 @@ import Mathbin.RingTheory.UniqueFactorizationDomain
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open scoped Classical BigOperators Polynomial
 
 open Finset
 
@@ -72,9 +72,11 @@ def degreeLT (n : ℕ) : Submodule R R[X] :=
 
 variable {R}
 
+#print Polynomial.mem_degreeLE /-
 theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degree f ≤ n := by
   simp only [degree_le, Submodule.mem_iInf, degree_le_iff_coeff_zero, LinearMap.mem_ker] <;> rfl
 #align polynomial.mem_degree_le Polynomial.mem_degreeLE
+-/
 
 @[mono]
 theorem degreeLE_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLE R m ≤ degreeLE R n := fun f hf =>
@@ -104,6 +106,7 @@ theorem degreeLE_eq_span_X_pow {n : ℕ} :
 #align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLE_eq_span_X_pow
 -/
 
+#print Polynomial.mem_degreeLT /-
 theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n :=
   by
   simp_rw [degree_lt, Submodule.mem_iInf, LinearMap.mem_ker, degree, Finset.max_eq_sup_coe,
@@ -111,6 +114,7 @@ theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n
     Ne, not_imp_not]
   rfl
 #align polynomial.mem_degree_lt Polynomial.mem_degreeLT
+-/
 
 @[mono]
 theorem degreeLT_mono {m n : ℕ} (H : m ≤ n) : degreeLT R m ≤ degreeLT R n := fun f hf =>
@@ -252,10 +256,12 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
 -/
 
+#print Polynomial.Monic.geom_sum' /-
 theorem Monic.geom_sum' {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.degree) {n : ℕ} (hn : n ≠ 0) :
     (∑ i in range n, P ^ i).Monic :=
   hP.geom_sum (natDegree_pos_iff_degree_pos.2 hdeg) hn
 #align polynomial.monic.geom_sum' Polynomial.Monic.geom_sum'
+-/
 
 #print Polynomial.monic_geom_sum_X /-
 theorem monic_geom_sum_X {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (X : R[X]) ^ i).Monic :=

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

@@ -72,22 +72,10 @@ def degreeLT (n : ℕ) : Submodule R R[X] :=
 
 variable {R}
 
-/- warning: polynomial.mem_degree_le -> Polynomial.mem_degreeLE is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : WithBot.{0} Nat} {f : Polynomial.{u1} R _inst_1}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) f (Polynomial.degreeLE.{u1} R _inst_1 n)) (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 f) n)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : WithBot.{0} Nat} {f : Polynomial.{u1} R _inst_1}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) f (Polynomial.degreeLE.{u1} R _inst_1 n)) (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 f) n)
-Case conversion may be inaccurate. Consider using '#align polynomial.mem_degree_le Polynomial.mem_degreeLEₓ'. -/
 theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degree f ≤ n := by
   simp only [degree_le, Submodule.mem_iInf, degree_le_iff_coeff_zero, LinearMap.mem_ker] <;> rfl
 #align polynomial.mem_degree_le Polynomial.mem_degreeLE
 
-/- warning: polynomial.degree_le_mono -> Polynomial.degreeLE_mono is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_mono Polynomial.degreeLE_monoₓ'. -/
 @[mono]
 theorem degreeLE_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLE R m ≤ degreeLE R n := fun f hf =>
   mem_degreeLE.2 (le_trans (mem_degreeLE.1 hf) H)
@@ -116,12 +104,6 @@ theorem degreeLE_eq_span_X_pow {n : ℕ} :
 #align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLE_eq_span_X_pow
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.mem_degree_lt Polynomial.mem_degreeLTₓ'. -/
 theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n :=
   by
   simp_rw [degree_lt, Submodule.mem_iInf, LinearMap.mem_ker, degree, Finset.max_eq_sup_coe,
@@ -130,12 +112,6 @@ theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n
   rfl
 #align polynomial.mem_degree_lt Polynomial.mem_degreeLT
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_mono Polynomial.degreeLT_monoₓ'. -/
 @[mono]
 theorem degreeLT_mono {m n : ℕ} (H : m ≤ n) : degreeLT R m ≤ degreeLT R n := fun f hf =>
   mem_degreeLT.2 (lt_of_lt_of_le (mem_degreeLT.1 hf) <| WithBot.coe_le_coe.2 H)
@@ -190,18 +166,12 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
 #align polynomial.degree_lt_equiv Polynomial.degreeLTEquiv
 -/
 
-/- warning: polynomial.degree_lt_equiv_eq_zero_iff_eq_zero -> Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zeroₓ'. -/
 @[simp]
 theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) :
     degreeLTEquiv _ _ ⟨p, hp⟩ = 0 ↔ p = 0 := by
   rw [LinearEquiv.map_eq_zero_iff, Submodule.mk_eq_zero]
 #align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero
 
-/- warning: polynomial.eval_eq_sum_degree_lt_equiv -> Polynomial.eval_eq_sum_degreeLTEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquivₓ'. -/
 theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
     p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
   by
@@ -222,12 +192,6 @@ theorem frange_zero : frange (0 : R[X]) = ∅ :=
 #align polynomial.frange_zero Polynomial.frange_zero
 -/
 
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 theorem mem_frange_iff {p : R[X]} {c : R} : c ∈ p.frange ↔ ∃ n ∈ p.support, c = p.coeff n := by
   simp [frange, eq_comm]
 #align polynomial.mem_frange_iff Polynomial.mem_frange_iff
@@ -243,12 +207,6 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
 #align polynomial.frange_one Polynomial.frange_one
 -/
 
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 theorem coeff_mem_frange (p : R[X]) (n : ℕ) (h : p.coeff n ≠ 0) : p.coeff n ∈ p.frange :=
   by
   simp only [frange, exists_prop, mem_support_iff, Finset.mem_image, Ne.def]
@@ -294,12 +252,6 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
 -/
 
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 theorem Monic.geom_sum' {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.degree) {n : ℕ} (hn : n ≠ 0) :
     (∑ i in range n, P ^ i).Monic :=
   hP.geom_sum (natDegree_pos_iff_degree_pos.2 hdeg) hn
@@ -320,12 +272,6 @@ section Ring
 
 variable [Ring R]
 
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 /-- Given a polynomial, return the polynomial whose coefficients are in
 the ring closure of the original coefficients. -/
 def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R)) :=
@@ -367,12 +313,6 @@ theorem support_restriction (p : R[X]) : support (restriction p) = support p :=
 #align polynomial.support_restriction Polynomial.support_restriction
 -/
 
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 @[simp]
 theorem map_restriction {R : Type u} [CommRing R] (p : R[X]) :
     p.restriction.map (algebraMap _ _) = p :=
@@ -392,12 +332,6 @@ theorem natDegree_restriction {p : R[X]} : (restriction p).natDegree = p.natDegr
 #align polynomial.nat_degree_restriction Polynomial.natDegree_restriction
 -/
 
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 @[simp]
 theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
   by
@@ -406,17 +340,11 @@ theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
   exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_restriction Polynomial.monic_restriction
 
-/- warning: polynomial.restriction_zero -> Polynomial.restriction_zero is a dubious translation:
-<too large>
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 @[simp]
 theorem restriction_zero : restriction (0 : R[X]) = 0 := by
   simp only [restriction, Finset.sum_empty, support_zero]
 #align polynomial.restriction_zero Polynomial.restriction_zero
 
-/- warning: polynomial.restriction_one -> Polynomial.restriction_one is a dubious translation:
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 @[simp]
 theorem restriction_one : restriction (1 : R[X]) = 1 :=
   ext fun i => Subtype.eq <| by rw [coeff_restriction', coeff_one, coeff_one] <;> split_ifs <;> rfl
@@ -424,12 +352,6 @@ theorem restriction_one : restriction (1 : R[X]) = 1 :=
 
 variable [Semiring S] {f : R →+* S} {x : S}
 
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 theorem eval₂_restriction {p : R[X]} :
     eval₂ f x p =
       eval₂ (f.comp (Subring.subtype (Subring.closure (p.frange : Set R)))) x p.restriction :=
@@ -442,12 +364,6 @@ section ToSubring
 
 variable (p : R[X]) (T : Subring R)
 
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 /-- Given a polynomial `p` and a subring `T` that contains the coefficients of `p`,
 return the corresponding polynomial whose coefficients are in `T`. -/
 def toSubring (hp : (↑p.frange : Set R) ⊆ T) : T[X] :=
@@ -461,12 +377,6 @@ variable (hp : (↑p.frange : Set R) ⊆ T)
 
 include hp
 
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 @[simp]
 theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n :=
   by
@@ -477,23 +387,11 @@ theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n
   · rfl
 #align polynomial.coeff_to_subring Polynomial.coeff_toSubring
 
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 @[simp]
 theorem coeff_toSubring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
   coeff_toSubring _ _ hp
 #align polynomial.coeff_to_subring' Polynomial.coeff_toSubring'
 
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 @[simp]
 theorem support_toSubring : support (toSubring p T hp) = support p :=
   by
@@ -503,32 +401,14 @@ theorem support_toSubring : support (toSubring p T hp) = support p :=
   exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.support_to_subring Polynomial.support_toSubring
 
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 @[simp]
 theorem degree_toSubring : (toSubring p T hp).degree = p.degree := by simp [degree]
 #align polynomial.degree_to_subring Polynomial.degree_toSubring
 
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 @[simp]
 theorem natDegree_toSubring : (toSubring p T hp).natDegree = p.natDegree := by simp [nat_degree]
 #align polynomial.nat_degree_to_subring Polynomial.natDegree_toSubring
 
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 @[simp]
 theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
   by
@@ -538,19 +418,10 @@ theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
 
 omit hp
 
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 @[simp]
 theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 := by ext i; simp
 #align polynomial.to_subring_zero Polynomial.toSubring_zero
 
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 @[simp]
 theorem toSubring_one :
     toSubring (1 : R[X]) T
@@ -559,12 +430,6 @@ theorem toSubring_one :
   ext fun i => Subtype.eq <| by rw [coeff_to_subring', coeff_one, coeff_one] <;> split_ifs <;> rfl
 #align polynomial.to_subring_one Polynomial.toSubring_one
 
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 @[simp]
 theorem map_toSubring : (p.toSubring T hp).map (Subring.subtype T) = p := by ext n; simp [coeff_map]
 #align polynomial.map_to_subring Polynomial.map_toSubring
@@ -573,24 +438,12 @@ end ToSubring
 
 variable (T : Subring R)
 
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 /-- Given a polynomial whose coefficients are in some subring, return
 the corresponding polynomial whose coefficients are in the ambient ring. -/
 def ofSubring (p : T[X]) : R[X] :=
   ∑ i in p.support, monomial i (p.coeff i : R)
 #align polynomial.of_subring Polynomial.ofSubring
 
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 theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff p n : T) :=
   by
   simp only [of_subring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
@@ -600,12 +453,6 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
   rfl
 #align polynomial.coeff_of_subring Polynomial.coeff_ofSubring
 
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 @[simp]
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T :=
   by
@@ -705,24 +552,12 @@ section CommSemiring
 
 variable [CommSemiring R] [Semiring S]
 
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 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself -/
 theorem polynomial_mem_ideal_of_coeff_mem_ideal (I : Ideal R[X]) (p : R[X])
     (hp : ∀ n : ℕ, p.coeff n ∈ I.comap (C : R →+* R[X])) : p ∈ I :=
   sum_C_mul_X_pow_eq p ▸ Submodule.sum_mem I fun n hn => I.mul_mem_right _ (hp n)
 #align ideal.polynomial_mem_ideal_of_coeff_mem_ideal Ideal.polynomial_mem_ideal_of_coeff_mem_ideal
 
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-Case conversion may be inaccurate. Consider using '#align ideal.mem_map_C_iff Ideal.mem_map_C_iffₓ'. -/
 /-- The push-forward of an ideal `I` of `R` to `R[X]` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
 theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
@@ -750,12 +585,6 @@ theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
     exact (I.map C : Ideal R[X]).mul_mem_left _ (mem_map_of_mem _ (hf n))
 #align ideal.mem_map_C_iff Ideal.mem_map_C_iff
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.ker_map_ring_hom Polynomial.ker_mapRingHomₓ'. -/
 theorem Polynomial.ker_mapRingHom (f : R →+* S) :
     (Polynomial.mapRingHom f).ker = f.ker.map (C : R →+* R[X]) :=
   by
@@ -766,12 +595,6 @@ theorem Polynomial.ker_mapRingHom (f : R →+* S) :
 
 variable (I : Ideal R[X])
 
-/- warning: ideal.mem_leading_coeff_nth -> Ideal.mem_leadingCoeffNth is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNthₓ'. -/
 theorem mem_leadingCoeffNth (n : ℕ) (x) :
     x ∈ I.leadingCoeffNth n ↔ ∃ p ∈ I, degree p ≤ n ∧ p.leadingCoeff = x :=
   by
@@ -796,12 +619,6 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
     · rw [Polynomial.leadingCoeff, ← coeff_mul_X_pow p (n - nat_degree p), this]
 #align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNth
 
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-Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zeroₓ'. -/
 theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :=
   (mem_leadingCoeffNth _ _ _).trans
     ⟨fun ⟨p, hpI, hpdeg, hpx⟩ => by
@@ -810,12 +627,6 @@ theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :
       fun hx => ⟨C x, hx, degree_C_le, leadingCoeff_C x⟩⟩
 #align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zero
 
-/- warning: ideal.leading_coeff_nth_mono -> Ideal.leadingCoeffNth_mono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_monoₓ'. -/
 theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤ I.leadingCoeffNth n :=
   by
   intro r hr
@@ -828,12 +639,6 @@ theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤
   exact le_rfl
 #align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_mono
 
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-Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff Ideal.mem_leadingCoeffₓ'. -/
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x :=
   by
   rw [leading_coeff, Submodule.mem_iSup_of_directed]
@@ -846,12 +651,6 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
       I.leading_coeff_nth_mono (Nat.le_add_left _ _)⟩
 #align ideal.mem_leading_coeff Ideal.mem_leadingCoeff
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_prod_mem_ideal_pow_tsub Polynomial.coeff_prod_mem_ideal_pow_tsubₓ'. -/
 /-- If `I` is an ideal, and `pᵢ` is a finite family of polynomials each satisfying
 `∀ k, (pᵢ)ₖ ∈ Iⁿⁱ⁻ᵏ` for some `nᵢ`, then `p = ∏ pᵢ` also satisfies `∀ k, pₖ ∈ Iⁿ⁻ᵏ` with `n = ∑ nᵢ`.
 -/
@@ -896,12 +695,6 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
 #align ideal.polynomial_not_is_field Ideal.polynomial_not_isField
 -/
 
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-Case conversion may be inaccurate. Consider using '#align ideal.eq_zero_of_constant_mem_of_maximal Ideal.eq_zero_of_constant_mem_of_maximalₓ'. -/
 /-- The only constant in a maximal ideal over a field is `0`. -/
 theorem eq_zero_of_constant_mem_of_maximal (hR : IsField R) (I : Ideal R[X]) [hI : I.IsMaximal]
     (x : R) (hx : C x ∈ I) : x = 0 :=
@@ -918,12 +711,6 @@ section CommRing
 
 variable [CommRing R]
 
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-Case conversion may be inaccurate. Consider using '#align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrimeₓ'. -/
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) ↔ IsPrime P :=
@@ -972,12 +759,6 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
         · apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hg hj)
 #align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrime
 
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-Case conversion may be inaccurate. Consider using '#align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrimeₓ'. -/
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_of_isPrime {P : Ideal R} (H : IsPrime P) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) :=
@@ -1006,12 +787,6 @@ variable (σ) {r : R}
 
 namespace Polynomial
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.prime_C_iff Polynomial.prime_C_iffₓ'. -/
 theorem prime_C_iff : Prime (C r) ↔ Prime r :=
   ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr =>
     by
@@ -1036,12 +811,6 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial
       convert(finSuccEquiv R d).toMulEquiv.symm.prime_iff
       rw [← fin_succ_equiv_comp_C_eq_C]; rfl
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iffₓ'. -/
 theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   ⟨comap_prime C constantCoeff (constantCoeff_C _), fun hr =>
     ⟨fun h => hr.1 <| by rw [← C_inj, h]; simp, fun h =>
@@ -1193,43 +962,22 @@ attribute [instance] Polynomial.isNoetherianRing
 
 namespace Polynomial
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_degree_pos Polynomial.exists_irreducible_of_degree_posₓ'. -/
 theorem exists_irreducible_of_degree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.degree) : ∃ g, Irreducible g ∧ g ∣ f :=
   WfDvdMonoid.exists_irreducible_factor (fun huf => ne_of_gt hf <| degree_eq_zero_of_isUnit huf)
     fun hf0 => not_lt_of_lt hf <| hf0.symm ▸ (@degree_zero R _).symm ▸ WithBot.bot_lt_coe _
 #align polynomial.exists_irreducible_of_degree_pos Polynomial.exists_irreducible_of_degree_pos
 
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 theorem exists_irreducible_of_natDegree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.natDegree) : ∃ g, Irreducible g ∧ g ∣ f :=
   exists_irreducible_of_degree_pos <| by contrapose! hf; exact nat_degree_le_of_degree_le hf
 #align polynomial.exists_irreducible_of_nat_degree_pos Polynomial.exists_irreducible_of_natDegree_pos
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zeroₓ'. -/
 theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDomain R]
     [WfDvdMonoid R] {f : R[X]} (hf : f.natDegree ≠ 0) : ∃ g, Irreducible g ∧ g ∣ f :=
   exists_irreducible_of_natDegree_pos <| Nat.pos_of_ne_zero hf
 #align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zero
 
-/- warning: polynomial.linear_independent_powers_iff_aeval -> Polynomial.linearIndependent_powers_iff_aeval is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aevalₓ'. -/
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 :=
   by
@@ -1252,9 +1000,6 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
 #align polynomial.disjoint_ker_aeval_of_coprime Polynomial.disjoint_ker_aeval_of_coprime
 -/
 
-/- warning: polynomial.sup_aeval_range_eq_top_of_coprime -> Polynomial.sup_aeval_range_eq_top_of_coprime is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprimeₓ'. -/
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=
   by
@@ -1270,9 +1015,6 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
     congr_arg (fun p : R[X] => aeval f p v) hpq'
 #align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprime
 
-/- warning: polynomial.sup_ker_aeval_le_ker_aeval_mul -> Polynomial.sup_ker_aeval_le_ker_aeval_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mulₓ'. -/
 theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     (aeval f p).ker ⊔ (aeval f q).ker ≤ (aeval f (p * q)).ker :=
   by
@@ -1285,9 +1027,6 @@ theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
   rw [LinearMap.mem_ker, ← hxy, LinearMap.map_add, h_eval_x, h_eval_y, add_zero]
 #align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mul
 
-/- warning: polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime -> Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprimeₓ'. -/
 theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X]}
     (hpq : IsCoprime p q) : (aeval f p).ker ⊔ (aeval f q).ker = (aeval f (p * q)).ker :=
   by
@@ -1349,12 +1088,6 @@ instance isNoetherianRing [Finite σ] [IsNoetherianRing R] : IsNoetherianRing (M
 #align mv_polynomial.is_noetherian_ring MvPolynomial.isNoetherianRing
 -/
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.no_zero_divisors_fin MvPolynomial.noZeroDivisors_finₓ'. -/
 /-- Auxiliary lemma:
 Multivariate polynomials over an integral domain
 with variables indexed by `fin n` form an integral domain.
@@ -1369,12 +1102,6 @@ theorem noZeroDivisors_fin (R : Type u) [CommSemiring R] [NoZeroDivisors R] :
     (MvPolynomial.finSuccEquiv R n).Injective.NoZeroDivisors _ (map_zero _) (map_mul _)
 #align mv_polynomial.no_zero_divisors_fin MvPolynomial.noZeroDivisors_fin
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.no_zero_divisors_of_finite MvPolynomial.noZeroDivisors_of_finiteₓ'. -/
 /-- Auxiliary definition:
 Multivariate polynomials in finitely many variables over an integral domain form an integral domain.
 This fact is proven by transport of structure from the `mv_polynomial.no_zero_divisors_fin`,
@@ -1413,9 +1140,6 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] : IsDomain (MvPoly
   exact AddMonoidAlgebra.nontrivial
   exact MvPolynomial.noZeroDivisors
 
-/- warning: mv_polynomial.map_mv_polynomial_eq_eval₂ -> MvPolynomial.map_mvPolynomial_eq_eval₂ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂ₓ'. -/
 theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :
     ϕ p = MvPolynomial.eval₂ (ϕ.comp MvPolynomial.C) (fun s => ϕ (MvPolynomial.X s)) p :=
@@ -1428,12 +1152,6 @@ theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ :
   simp only [monomial_eq, ϕ.map_pow, ϕ.map_prod, ϕ.comp_apply, ϕ.map_mul, Finsupp.prod_pow]
 #align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂
 
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-Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_ideal_of_coeff_mem_ideal MvPolynomial.mem_ideal_of_coeff_mem_idealₓ'. -/
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself,
 multivariate version. -/
 theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPolynomial σ R)
@@ -1448,12 +1166,6 @@ theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPoly
   simpa [Ideal.mem_comap] using hcoe m
 #align mv_polynomial.mem_ideal_of_coeff_mem_ideal MvPolynomial.mem_ideal_of_coeff_mem_ideal
 
-/- warning: mv_polynomial.mem_map_C_iff -> MvPolynomial.mem_map_C_iff is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {f : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) f (Ideal.map.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m f) I)
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_C_iffₓ'. -/
 /-- The push-forward of an ideal `I` of `R` to `mv_polynomial σ R` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
 theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
@@ -1486,9 +1198,6 @@ theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
     exact hf m
 #align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_C_iff
 
-/- warning: mv_polynomial.ker_map -> MvPolynomial.ker_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.ker_map MvPolynomial.ker_mapₓ'. -/
 theorem ker_map (f : R →+* S) :
     (map f : MvPolynomial σ R →+* MvPolynomial σ S).ker = f.ker.map (C : R →+* MvPolynomial σ R) :=
   by

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

@@ -98,8 +98,7 @@ theorem degreeLE_eq_span_X_pow {n : ℕ} :
     degreeLE R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) :=
   by
   apply le_antisymm
-  · intro p hp
-    replace hp := mem_degree_le.1 hp
+  · intro p hp; replace hp := mem_degree_le.1 hp
     rw [← Polynomial.sum_monomial_eq p, Polynomial.sum]
     refine' Submodule.sum_mem _ fun k hk => _
     show monomial _ _ ∈ _
@@ -147,8 +146,7 @@ theorem degreeLT_eq_span_X_pow {n : ℕ} :
     degreeLT R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) :=
   by
   apply le_antisymm
-  · intro p hp
-    replace hp := mem_degree_lt.1 hp
+  · intro p hp; replace hp := mem_degree_lt.1 hp
     rw [← Polynomial.sum_monomial_eq p, Polynomial.sum]
     refine' Submodule.sum_mem _ fun k hk => _
     show monomial _ _ ∈ _
@@ -174,31 +172,21 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
       (degreeLT R n).sum_mem fun i _ =>
         mem_degreeLT.mpr
           (lt_of_le_of_lt (degree_monomial_le i (f i)) (WithBot.coe_lt_coe.mpr i.is_lt))⟩
-  map_add' p q := by
-    ext
-    rw [Submodule.coe_add, coeff_add]
-    rfl
-  map_smul' x p := by
-    ext
-    rw [Submodule.coe_smul, coeff_smul]
-    rfl
+  map_add' p q := by ext; rw [Submodule.coe_add, coeff_add]; rfl
+  map_smul' x p := by ext; rw [Submodule.coe_smul, coeff_smul]; rfl
   left_inv := by
     rintro ⟨p, hp⟩; ext1
     simp only [Submodule.coe_mk]
     by_cases hp0 : p = 0
-    · subst hp0
-      simp only [coeff_zero, LinearMap.map_zero, Finset.sum_const_zero]
+    · subst hp0; simp only [coeff_zero, LinearMap.map_zero, Finset.sum_const_zero]
     rw [mem_degree_lt, degree_eq_nat_degree hp0, WithBot.coe_lt_coe] at hp
     conv_rhs => rw [p.as_sum_range' n hp, ← Fin.sum_univ_eq_sum_range]
   right_inv := by
     intro f; ext i
     simp only [finset_sum_coeff, Submodule.coe_mk]
     rw [Finset.sum_eq_single i, coeff_monomial, if_pos rfl]
-    · rintro j - hji
-      rw [coeff_monomial, if_neg]
-      rwa [← Fin.ext_iff]
-    · intro h
-      exact (h (Finset.mem_univ _)).elim
+    · rintro j - hji; rw [coeff_monomial, if_neg]; rwa [← Fin.ext_iff]
+    · intro h; exact (h (Finset.mem_univ _)).elim
 #align polynomial.degree_lt_equiv Polynomial.degreeLTEquiv
 -/
 
@@ -300,8 +288,7 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
   rw [Finset.sup_lt_iff]
   · simp only [Finset.mem_range, degree_eq_nat_degree (hP.pow _).NeZero, WithBot.coe_lt_coe,
       hP.nat_degree_pow]
-    intro k
-    exact nsmul_lt_nsmul hdeg
+    intro k; exact nsmul_lt_nsmul hdeg
   · rw [bot_lt_iff_ne_bot, Ne.def, degree_eq_bot]
     exact (hP.pow _).NeZero
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
@@ -357,8 +344,7 @@ theorem coeff_restriction {p : R[X]} {n : ℕ} : ↑(coeff (restriction p) n) =
   simp only [restriction, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
     Ne.def, ite_not]
   split_ifs
-  · rw [h]
-    rfl
+  · rw [h]; rfl
   · rfl
 #align polynomial.coeff_restriction Polynomial.coeff_restriction
 -/
@@ -377,10 +363,7 @@ theorem support_restriction (p : R[X]) : support (restriction p) = support p :=
   ext i
   simp only [mem_support_iff, not_iff_not, Ne.def]
   conv_rhs => rw [← coeff_restriction]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.support_restriction Polynomial.support_restriction
 -/
 
@@ -420,10 +403,7 @@ theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
   by
   simp only [monic, leading_coeff, nat_degree_restriction]
   rw [← @coeff_restriction _ _ p]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_restriction Polynomial.monic_restriction
 
 /- warning: polynomial.restriction_zero -> Polynomial.restriction_zero is a dubious translation:
@@ -493,8 +473,7 @@ theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n
   simp only [to_subring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
     Ne.def, ite_not]
   split_ifs
-  · rw [h]
-    rfl
+  · rw [h]; rfl
   · rfl
 #align polynomial.coeff_to_subring Polynomial.coeff_toSubring
 
@@ -521,10 +500,7 @@ theorem support_toSubring : support (toSubring p T hp) = support p :=
   ext i
   simp only [mem_support_iff, not_iff_not, Ne.def]
   conv_rhs => rw [← coeff_to_subring p T hp]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.support_to_subring Polynomial.support_toSubring
 
 /- warning: polynomial.degree_to_subring -> Polynomial.degree_toSubring is a dubious translation:
@@ -557,10 +533,7 @@ Case conversion may be inaccurate. Consider using '#align polynomial.monic_to_su
 theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
   by
   simp_rw [monic, leading_coeff, nat_degree_to_subring, ← coeff_to_subring p T hp]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H]; rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_to_subring Polynomial.monic_toSubring
 
 omit hp
@@ -569,10 +542,7 @@ omit hp
 <too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.to_subring_zero Polynomial.toSubring_zeroₓ'. -/
 @[simp]
-theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 :=
-  by
-  ext i
-  simp
+theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 := by ext i; simp
 #align polynomial.to_subring_zero Polynomial.toSubring_zero
 
 /- warning: polynomial.to_subring_one -> Polynomial.toSubring_one is a dubious translation:
@@ -596,10 +566,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.map.{u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) R (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Ring.toSemiring.{u1} R _inst_1) (Subring.subtype.{u1} R _inst_1 T) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) p
 Case conversion may be inaccurate. Consider using '#align polynomial.map_to_subring Polynomial.map_toSubringₓ'. -/
 @[simp]
-theorem map_toSubring : (p.toSubring T hp).map (Subring.subtype T) = p :=
-  by
-  ext n
-  simp [coeff_map]
+theorem map_toSubring : (p.toSubring T hp).map (Subring.subtype T) = p := by ext n; simp [coeff_map]
 #align polynomial.map_to_subring Polynomial.map_toSubring
 
 end ToSubring
@@ -694,9 +661,7 @@ def ofPolynomial (I : Ideal R[X]) : Submodule R R[X]
   carrier := I.carrier
   zero_mem' := I.zero_mem
   add_mem' _ _ := I.add_mem
-  smul_mem' c x H := by
-    rw [← C_mul']
-    exact I.mul_mem_left _ H
+  smul_mem' c x H := by rw [← C_mul']; exact I.mul_mem_left _ H
 #align ideal.of_polynomial Ideal.ofPolynomial
 -/
 
@@ -819,8 +784,7 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
       rw [leading_coeff_zero, eq_comm]
       exact coeff_eq_zero_of_degree_lt hpdeg
     · refine' ⟨p, hpI, le_of_eq hpdeg, _⟩
-      rw [Polynomial.leadingCoeff, nat_degree, hpdeg]
-      rfl
+      rw [Polynomial.leadingCoeff, nat_degree, hpdeg]; rfl
   · rintro ⟨p, hpI, hpdeg, rfl⟩
     have : nat_degree p + (n - nat_degree p) = n :=
       add_tsub_cancel_of_le (nat_degree_le_of_degree_le hpdeg)
@@ -874,11 +838,8 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
   by
   rw [leading_coeff, Submodule.mem_iSup_of_directed]
   simp only [mem_leading_coeff_nth]
-  · constructor
-    · rintro ⟨i, p, hpI, hpdeg, rfl⟩
-      exact ⟨p, hpI, rfl⟩
-    rintro ⟨p, hpI, rfl⟩
-    exact ⟨nat_degree p, p, hpI, degree_le_nat_degree, rfl⟩
+  · constructor; · rintro ⟨i, p, hpI, hpdeg, rfl⟩; exact ⟨p, hpI, rfl⟩
+    rintro ⟨p, hpI, rfl⟩; exact ⟨nat_degree p, p, hpI, degree_le_nat_degree, rfl⟩
   intro i j;
   exact
     ⟨i + j, I.leading_coeff_nth_mono (Nat.le_add_right _ _),
@@ -980,17 +941,13 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     · rintro h (- | n)
       · simpa only [coeff_C_zero] using h
       · simp only [coeff_C_ne_zero (Nat.succ_ne_zero _), Submodule.zero_mem]
-    · intro h
-      simpa only [coeff_C_zero] using h 0
+    · intro h; simpa only [coeff_C_zero] using h 0
   · intro h
     constructor
     · rw [Ne.def, eq_top_iff_one, mem_map_C_iff, not_forall]
       use 0
-      rw [coeff_one_zero, ← eq_top_iff_one]
-      exact h.1
-    · intro f g
-      simp only [mem_map_C_iff]
-      contrapose!
+      rw [coeff_one_zero, ← eq_top_iff_one]; exact h.1
+    · intro f g; simp only [mem_map_C_iff]; contrapose!
       rintro ⟨hf, hg⟩
       classical
         let m := Nat.find hf
@@ -998,9 +955,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
         refine' ⟨m + n, _⟩
         rw [coeff_mul, ← Finset.insert_erase ((@Finset.Nat.mem_antidiagonal _ (m, n)).mpr rfl),
           Finset.sum_insert (Finset.not_mem_erase _ _), (P.add_mem_iff_left _).Not]
-        · apply mt h.2
-          rw [not_or]
-          exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
+        · apply mt h.2; rw [not_or]; exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
         apply P.sum_mem
         rintro ⟨i, j⟩ hij
         rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij
@@ -1009,17 +964,12 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
           by
           rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
           rintro (hmi | rfl)
-          · rw [← not_le]
-            intro hnj
-            exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
+          · rw [← not_le]; intro hnj; exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
           ·
             simpa only [eq_self_iff_true, not_true, false_or_iff, add_right_inj,
               not_and_self_iff] using hij
-        · rw [mul_comm]
-          apply P.mul_mem_left
-          exact Classical.not_not.1 (Nat.find_min hf hi)
-        · apply P.mul_mem_left
-          exact Classical.not_not.1 (Nat.find_min hg hj)
+        · rw [mul_comm]; apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hf hi)
+        · apply P.mul_mem_left; exact Classical.not_not.1 (Nat.find_min hg hj)
 #align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrime
 
 /- warning: ideal.is_prime_map_C_of_is_prime -> Ideal.isPrime_map_C_of_isPrime is a dubious translation:
@@ -1079,16 +1029,12 @@ namespace MvPolynomial
 private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   by
   rw [(rename_equiv R (Fintype.equivFin σ)).toMulEquiv.prime_iff]
-  convert_to Prime (C r) ↔ _;
-  · congr
-    apply rename_C
-  · symm
-    induction' Fintype.card σ with d hd
+  convert_to Prime (C r) ↔ _; · congr ; apply rename_C
+  · symm; induction' Fintype.card σ with d hd
     · exact (is_empty_alg_equiv R (Fin 0)).toMulEquiv.symm.prime_iff
     · rw [hd, ← Polynomial.prime_C_iff]
       convert(finSuccEquiv R d).toMulEquiv.symm.prime_iff
-      rw [← fin_succ_equiv_comp_C_eq_C]
-      rfl
+      rw [← fin_succ_equiv_comp_C_eq_C]; rfl
 
 /- warning: mv_polynomial.prime_C_iff -> MvPolynomial.prime_C_iff is a dubious translation:
 lean 3 declaration is
@@ -1098,24 +1044,14 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iffₓ'. -/
 theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   ⟨comap_prime C constantCoeff (constantCoeff_C _), fun hr =>
-    ⟨fun h =>
-      hr.1 <| by
-        rw [← C_inj, h]
-        simp,
-      fun h =>
-      hr.2.1 <| by
-        rw [← constant_coeff_C _ r]
-        exact h.map _,
-      fun a b hd => by
+    ⟨fun h => hr.1 <| by rw [← C_inj, h]; simp, fun h =>
+      hr.2.1 <| by rw [← constant_coeff_C _ r]; exact h.map _, fun a b hd =>
+      by
       obtain ⟨s, a', b', rfl, rfl⟩ := exists_finset_rename₂ a b
-      rw [← algebra_map_eq] at hd
-      have : algebraMap R _ r ∣ a' * b' :=
-        by
-        convert(kill_compl Subtype.coe_injective).toRingHom.map_dvd hd
-        simpa
-        simp
-      rw [← rename_C (coe : s → σ)]
-      let f := (rename (coe : s → σ)).toRingHom
+      rw [← algebra_map_eq] at hd;
+      have : algebraMap R _ r ∣ a' * b' := by
+        convert(kill_compl Subtype.coe_injective).toRingHom.map_dvd hd; simpa; simp
+      rw [← rename_C (coe : s → σ)]; let f := (rename (coe : s → σ)).toRingHom
       exact (((prime_C_iff_of_fintype s).2 hr).2.2 a' b' this).imp f.map_dvd f.map_dvd⟩⟩
 #align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iff
 
@@ -1134,13 +1070,8 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     suffices (rename coe).toRingHom = eqv.to_alg_hom.to_ring_hom.comp C by
       apply RingHom.congr_fun this
     · apply ring_hom_ext
-      · intro
-        dsimp [eqv]
-        erw [iter_to_sum_C_C, rename_C, rename_C]
-      · intro
-        dsimp [eqv]
-        erw [iter_to_sum_C_X, rename_X, rename_X]
-        rfl
+      · intro ; dsimp [eqv]; erw [iter_to_sum_C_C, rename_C, rename_C]
+      · intro ; dsimp [eqv]; erw [iter_to_sum_C_X, rename_X, rename_X]; rfl
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
 -/
 
@@ -1212,31 +1143,21 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
           by
           have : Submodule.span R[X] ↑s = Ideal.span ↑s := by rfl
           rw [this]
-          intro p hp
-          generalize hn : p.nat_degree = k
+          intro p hp; generalize hn : p.nat_degree = k
           induction' k using Nat.strong_induction_on with k ih generalizing p
           cases le_or_lt k N
-          · subst k
+          · subst k;
             refine'
               hs2
                 ⟨Polynomial.mem_degreeLE.2
                     (le_trans Polynomial.degree_le_natDegree <| WithBot.coe_le_coe.2 h),
                   hp⟩
-          · have hp0 : p ≠ 0 := by
-              rintro rfl
-              cases hn
-              exact Nat.not_lt_zero _ h
+          · have hp0 : p ≠ 0 := by rintro rfl; cases hn; exact Nat.not_lt_zero _ h
             have : (0 : R) ≠ 1 := by
-              intro h
-              apply hp0
-              ext i
-              refine' (mul_one _).symm.trans _
-              rw [← h, MulZeroClass.mul_zero]
-              rfl
+              intro h; apply hp0; ext i; refine' (mul_one _).symm.trans _
+              rw [← h, MulZeroClass.mul_zero]; rfl
             haveI : Nontrivial R := ⟨⟨0, 1, this⟩⟩
-            have : p.leading_coeff ∈ I.leading_coeff_nth N :=
-              by
-              rw [HN]
+            have : p.leading_coeff ∈ I.leading_coeff_nth N := by rw [HN];
               exact
                 hm2 k
                   ((I.mem_leading_coeff_nth _ _).2
@@ -1244,10 +1165,8 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
             rw [I.mem_leading_coeff_nth] at this
             rcases this with ⟨q, hq, hdq, hlqp⟩
             have hq0 : q ≠ 0 := by
-              intro H
-              rw [← Polynomial.leadingCoeff_eq_zero] at H
-              rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H
-              exact hp0 H
+              intro H; rw [← Polynomial.leadingCoeff_eq_zero] at H
+              rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H; exact hp0 H
             have h1 : p.degree = (q * Polynomial.X ^ (k - q.nat_degree)).degree :=
               by
               rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
@@ -1263,8 +1182,7 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
             rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.nat_degree))]
             refine' (Ideal.span ↑s).add_mem _ ((Ideal.span ↑s).mul_mem_right _ _)
             · by_cases hpq : p - q * Polynomial.X ^ (k - q.nat_degree) = 0
-              · rw [hpq]
-                exact Ideal.zero_mem _
+              · rw [hpq]; exact Ideal.zero_mem _
               refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
               rwa [Polynomial.degree_eq_natDegree hpq, WithBot.coe_lt_coe, hn] at this
             exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
@@ -1295,9 +1213,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_nat_degree_pos Polynomial.exists_irreducible_of_natDegree_posₓ'. -/
 theorem exists_irreducible_of_natDegree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.natDegree) : ∃ g, Irreducible g ∧ g ∣ f :=
-  exists_irreducible_of_degree_pos <| by
-    contrapose! hf
-    exact nat_degree_le_of_degree_le hf
+  exists_irreducible_of_degree_pos <| by contrapose! hf; exact nat_degree_le_of_degree_le hf
 #align polynomial.exists_irreducible_of_nat_degree_pos Polynomial.exists_irreducible_of_natDegree_pos
 
 /- warning: polynomial.exists_irreducible_of_nat_degree_ne_zero -> Polynomial.exists_irreducible_of_natDegree_ne_zero is a dubious translation:
@@ -1484,9 +1400,7 @@ instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
             (Subtype.map id (Finset.subset_union_right s t) : { x // x ∈ t } → { x // x ∈ s ∪ t })
             q =
         0 :=
-      by
-      apply rename_injective _ Subtype.val_injective
-      simpa using h
+      by apply rename_injective _ Subtype.val_injective; simpa using h
     letI := MvPolynomial.noZeroDivisors_of_finite R { x // x ∈ s ∪ t }
     rw [mul_eq_zero] at this
     cases this <;> [left;right]

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

@@ -203,10 +203,7 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
 -/
 
 /- warning: polynomial.degree_lt_equiv_eq_zero_iff_eq_zero -> Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R 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u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zeroₓ'. -/
 @[simp]
 theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) :
@@ -215,10 +212,7 @@ theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degre
 #align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero
 
 /- warning: polynomial.eval_eq_sum_degree_lt_equiv -> Polynomial.eval_eq_sum_degreeLTEquiv is a dubious translation:
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_inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R 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_inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} 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(Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 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_inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquivₓ'. -/
 theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
     p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
@@ -433,10 +427,7 @@ theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
 #align polynomial.monic_restriction Polynomial.monic_restriction
 
 /- warning: polynomial.restriction_zero -> Polynomial.restriction_zero is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align polynomial.restriction_zero Polynomial.restriction_zeroₓ'. -/
 @[simp]
 theorem restriction_zero : restriction (0 : R[X]) = 0 := by
@@ -444,10 +435,7 @@ theorem restriction_zero : restriction (0 : R[X]) = 0 := by
 #align polynomial.restriction_zero Polynomial.restriction_zero
 
 /- warning: polynomial.restriction_one -> Polynomial.restriction_one is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align polynomial.restriction_one Polynomial.restriction_oneₓ'. -/
 @[simp]
 theorem restriction_one : restriction (1 : R[X]) = 1 :=
@@ -578,10 +566,7 @@ theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
 omit hp
 
 /- warning: polynomial.to_subring_zero -> Polynomial.toSubring_zero is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align polynomial.to_subring_zero Polynomial.toSubring_zeroₓ'. -/
 @[simp]
 theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 :=
@@ -674,17 +659,17 @@ section ModByMonic
 
 variable {q : R[X]}
 
-#print Polynomial.mem_ker_mod_by_monic /-
-theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q).ker ↔ q ∣ p :=
+#print Polynomial.mem_ker_modByMonic /-
+theorem mem_ker_modByMonic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q).ker ↔ q ∣ p :=
   LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
-#align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monic
+#align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_modByMonic
 -/
 
 #print Polynomial.ker_modByMonicHom /-
 @[simp]
 theorem ker_modByMonicHom (hq : q.Monic) :
     (Polynomial.modByMonicHom q).ker = (Ideal.span {q}).restrictScalars R :=
-  Submodule.ext fun f => (mem_ker_mod_by_monic hq).trans Ideal.mem_span_singleton.symm
+  Submodule.ext fun f => (mem_ker_modByMonic hq).trans Ideal.mem_span_singleton.symm
 #align polynomial.ker_mod_by_monic_hom Polynomial.ker_modByMonicHom
 -/
 
@@ -1104,7 +1089,6 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial
       convert(finSuccEquiv R d).toMulEquiv.symm.prime_iff
       rw [← fin_succ_equiv_comp_C_eq_C]
       rfl
-#align mv_polynomial.prime_C_iff_of_fintype mv_polynomial.prime_C_iff_of_fintype
 
 /- warning: mv_polynomial.prime_C_iff -> MvPolynomial.prime_C_iff is a dubious translation:
 lean 3 declaration is
@@ -1328,10 +1312,7 @@ theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDom
 #align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zero
 
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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aevalₓ'. -/
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 :=
@@ -1356,10 +1337,7 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
 -/
 
 /- warning: polynomial.sup_aeval_range_eq_top_of_coprime -> Polynomial.sup_aeval_range_eq_top_of_coprime is a dubious translation:
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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprimeₓ'. -/
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=
@@ -1377,10 +1355,7 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
 #align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprime
 
 /- warning: polynomial.sup_ker_aeval_le_ker_aeval_mul -> Polynomial.sup_ker_aeval_le_ker_aeval_mul is a dubious translation:
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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 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(CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M 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_inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mulₓ'. -/
 theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     (aeval f p).ker ⊔ (aeval f q).ker ≤ (aeval f (p * q)).ker :=
@@ -1395,10 +1370,7 @@ theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
 #align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mul
 
 /- warning: polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime -> Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime is a dubious translation:
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_inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M 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_inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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_inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprimeₓ'. -/
 theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X]}
     (hpq : IsCoprime p q) : (aeval f p).ker ⊔ (aeval f q).ker = (aeval f (p * q)).ker :=
@@ -1528,10 +1500,7 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] : IsDomain (MvPoly
   exact MvPolynomial.noZeroDivisors
 
 /- warning: mv_polynomial.map_mv_polynomial_eq_eval₂ -> MvPolynomial.map_mvPolynomial_eq_eval₂ is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂ₓ'. -/
 theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :
@@ -1604,10 +1573,7 @@ theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
 #align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_C_iff
 
 /- warning: mv_polynomial.ker_map -> MvPolynomial.ker_map is a dubious translation:
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-but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))), Eq.{max (succ u2) (succ u3)} (Ideal.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u2 u3, max u3 u1, max (max u2 u3) u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ 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(MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.ker.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.ker_map MvPolynomial.ker_mapₓ'. -/
 theorem ker_map (f : R →+* S) :
     (map f : MvPolynomial σ R →+* MvPolynomial σ S).ker = f.ker.map (C : R →+* MvPolynomial σ R) :=
@@ -1649,7 +1615,6 @@ private theorem unique_factorization_monoid_of_fintype [Fintype σ] :
       infer_instance
     · apply (finSuccEquiv D d).toMulEquiv.symm.UniqueFactorizationMonoid
       exact Polynomial.uniqueFactorizationMonoid
-#align mv_polynomial.unique_factorization_monoid_of_fintype mv_polynomial.unique_factorization_monoid_of_fintype
 
 instance (priority := 100) : UniqueFactorizationMonoid (MvPolynomial σ D) :=
   by

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

@@ -206,7 +206,7 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
 lean 3 declaration is
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_inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((Fin n) -> R) (coeFn.{succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) 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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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} 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_inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => 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(RingHomInvPair.ids.{u1} R _inst_1)) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (OfNat.ofNat.{u1} ((Fin n) -> R) 0 (OfNat.mk.{u1} ((Fin n) -> R) 0 (Zero.zero.{u1} ((Fin n) -> R) (Pi.instZero.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (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 : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 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(DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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 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(Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (Pi.instZero.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (fun (_x : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x 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(Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (SMulZeroClass.toSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) 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_inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R 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(Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 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(Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R 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((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (Pi.instZero.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zeroₓ'. -/
 @[simp]
 theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) :
@@ -218,7 +218,7 @@ theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degre
 lean 3 declaration is
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_inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Finset.sum.{u1, 0} R (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, 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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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) 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(Pi.Function.module.{0, u1, u1} (Fin n) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i))))
 but is expected to have type
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(Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) 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(Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R 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(Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (Fin.val n i))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Finset.sum.{u1, 0} R (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (fun (_x : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (SMulZeroClass.toSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R 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(Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) 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(Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (Fin.val n i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquivₓ'. -/
 theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
     p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
@@ -1331,7 +1331,7 @@ theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDom
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R M (fun (n : Nat) => coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) f n) v) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (forall (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Eq.{succ u2} M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_3))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (fun (n : Nat) => FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.monoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) f n) v) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) _inst_3) _inst_4) (forall (p : Polynomial.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) _inst_3)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) (fun (n : Nat) => FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.monoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) f n) v) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) _inst_3) _inst_4) (forall (p : Polynomial.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) 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(Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => M) v) _inst_3)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aevalₓ'. -/
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 :=
@@ -1359,7 +1359,7 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R 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(AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) 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(CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprimeₓ'. -/
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=
@@ -1380,7 +1380,7 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) 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u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R 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_inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mulₓ'. -/
 theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     (aeval f p).ker ⊔ (aeval f q).ker ≤ (aeval f (p * q)).ker :=
@@ -1398,7 +1398,7 @@ theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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_inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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_inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) 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R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} 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(Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) 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u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprimeₓ'. -/
 theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X]}
     (hpq : IsCoprime p q) : (aeval f p).ker ⊔ (aeval f q).ker = (aeval f (p * q)).ker :=
@@ -1517,7 +1517,7 @@ instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
       simpa using h
     letI := MvPolynomial.noZeroDivisors_of_finite R { x // x ∈ s ∪ t }
     rw [mul_eq_zero] at this
-    cases this <;> [left, right]
+    cases this <;> [left;right]
     all_goals simpa using congr_arg (rename Subtype.val) this⟩
 
 /-- The multivariate polynomial ring over an integral domain is an integral domain. -/

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

@@ -851,7 +851,7 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) I)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) I)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) I)
 Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zeroₓ'. -/
 theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :=
   (mem_leadingCoeffNth _ _ _).trans
@@ -954,7 +954,7 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (IsField.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (forall (I : Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) [hI : Ideal.IsMaximal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I] (x : R), (Membership.Mem.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) I) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (IsField.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (forall (I : Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) [hI : Ideal.IsMaximal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I] (x : R), (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) I) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (IsField.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (forall (I : Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) [hI : Ideal.IsMaximal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I] (x : R), (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) I) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align ideal.eq_zero_of_constant_mem_of_maximal Ideal.eq_zero_of_constant_mem_of_maximalₓ'. -/
 /-- The only constant in a maximal ideal over a field is `0`. -/
 theorem eq_zero_of_constant_mem_of_maximal (hR : IsField R) (I : Ideal R[X]) [hI : I.IsMaximal]
@@ -1075,7 +1075,7 @@ namespace Polynomial
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (Polynomial.commRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (Polynomial.commRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.prime_C_iff Polynomial.prime_C_iffₓ'. -/
 theorem prime_C_iff : Prime (C r) ↔ Prime r :=
   ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr =>
@@ -1110,7 +1110,7 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial
 lean 3 declaration is
   forall {R : Type.{u1}} (σ : Type.{u2}) [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
 but is expected to have type
-  forall {R : Type.{u1}} (σ : Type.{u2}) [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) r) (CommSemiring.toCommMonoidWithZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) r) (CommRing.toCommSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) r) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
+  forall {R : Type.{u1}} (σ : Type.{u2}) [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) r) (CommSemiring.toCommMonoidWithZero.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) r) (CommRing.toCommSemiring.{max u1 u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) r) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, max (succ u2) (succ u1)} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iffₓ'. -/
 theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   ⟨comap_prime C constantCoeff (constantCoeff_C _), fun hr =>
@@ -1531,7 +1531,7 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] : IsDomain (MvPoly
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {S : Type.{u3}} [_inst_5 : CommRing.{u3} S] [_inst_6 : Finite.{succ u2} σ] (ϕ : RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) (p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)), Eq.{succ u3} S (coeFn.{max (succ (max u2 u1)) (succ u3), max (succ (max u2 u1)) (succ u3)} (RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) (fun (_x : RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> S) (RingHom.hasCoeToFun.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) ϕ p) (MvPolynomial.eval₂.{u1, u3, u2} R S σ (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u3} S _inst_5) (RingHom.comp.{u1, max u2 u1, u3} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5))) ϕ (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (s : σ) => coeFn.{max (succ (max u2 u1)) (succ u3), max (succ (max u2 u1)) (succ u3)} (RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) (fun (_x : RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> S) (RingHom.hasCoeToFun.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) ϕ (MvPolynomial.X.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) s)) p)
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_5 : CommRing.{u1} S] [_inst_6 : Finite.{succ u3} σ] (ϕ : RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) p) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) ϕ p) (MvPolynomial.eval₂.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} S _inst_5) (RingHom.comp.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) ϕ (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (s : σ) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, 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(CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) ϕ (MvPolynomial.X.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s)) p)
+  forall {R : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_5 : CommRing.{u1} S] [_inst_6 : Finite.{succ u3} σ] (ϕ : RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) p) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) ϕ p) (MvPolynomial.eval₂.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} S _inst_5) (RingHom.comp.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) ϕ (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (s : σ) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} 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_inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) ϕ (MvPolynomial.X.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s)) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂ₓ'. -/
 theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :

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

@@ -674,27 +674,19 @@ section ModByMonic
 
 variable {q : R[X]}
 
-/- warning: polynomial.mem_ker_mod_by_monic -> Polynomial.mem_ker_mod_by_monic is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R 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-Case conversion may be inaccurate. Consider using '#align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monicₓ'. -/
+#print Polynomial.mem_ker_mod_by_monic /-
 theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q).ker ↔ q ∣ p :=
   LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
 #align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monic
+-/
 
-/- warning: polynomial.ker_mod_by_monic_hom -> Polynomial.ker_modByMonicHom is a dubious translation:
-lean 3 declaration is
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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.isScalarTower_right.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) q))))
-Case conversion may be inaccurate. Consider using '#align polynomial.ker_mod_by_monic_hom Polynomial.ker_modByMonicHomₓ'. -/
+#print Polynomial.ker_modByMonicHom /-
 @[simp]
 theorem ker_modByMonicHom (hq : q.Monic) :
     (Polynomial.modByMonicHom q).ker = (Ideal.span {q}).restrictScalars R :=
   Submodule.ext fun f => (mem_ker_mod_by_monic hq).trans Ideal.mem_span_singleton.symm
 #align polynomial.ker_mod_by_monic_hom Polynomial.ker_modByMonicHom
+-/
 
 end ModByMonic
 
@@ -812,7 +804,7 @@ theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.ker.{u1, u2, max u1 u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} S _inst_2) (RingHom.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.mapRingHom.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 f)) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u2} (Submodule.{u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.ker.{u2, u1, u2, u1, max u2 u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f) (LinearMap.{u2, u1, u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u1, u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f)) (RingHom.toSemilinearMap.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f))) (Ideal.map.{u2, u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.C.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.ker.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) f))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u2} (Submodule.{u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.ker.{u2, u1, u2, u1, max u2 u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f) (LinearMap.{u2, u1, u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2))) (LinearMap.semilinearMapClass.{u2, u1, u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f)) (RingHom.toSemilinearMap.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f))) (Ideal.map.{u2, u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.C.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.ker.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)) f))
 Case conversion may be inaccurate. Consider using '#align polynomial.ker_map_ring_hom Polynomial.ker_mapRingHomₓ'. -/
 theorem Polynomial.ker_mapRingHom (f : R →+* S) :
     (Polynomial.mapRingHom f).ker = f.ker.map (C : R →+* R[X]) :=
@@ -1339,7 +1331,7 @@ theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDom
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R M (fun (n : Nat) => coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) f n) v) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (forall (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Eq.{succ u2} M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) 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 but is expected to have type
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_inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) _inst_3)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (fun (n : Nat) => FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => M) v) _inst_3)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aevalₓ'. -/
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 :=
@@ -1367,7 +1359,7 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R 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(Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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_inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprimeₓ'. -/
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=
@@ -1388,7 +1380,7 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} 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_inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 but is expected to have type
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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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_inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mulₓ'. -/
 theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     (aeval f p).ker ⊔ (aeval f q).ker ≤ (aeval f (p * q)).ker :=
@@ -1406,7 +1398,7 @@ theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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_inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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_inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprimeₓ'. -/
 theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X]}
     (hpq : IsCoprime p q) : (aeval f p).ker ⊔ (aeval f q).ker = (aeval f (p * q)).ker :=

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

@@ -72,15 +72,19 @@ def degreeLT (n : ℕ) : Submodule R R[X] :=
 
 variable {R}
 
-#print Polynomial.mem_degreeLE /-
+/- warning: polynomial.mem_degree_le -> Polynomial.mem_degreeLE is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : WithBot.{0} Nat} {f : Polynomial.{u1} R _inst_1}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) f (Polynomial.degreeLE.{u1} R _inst_1 n)) (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 f) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : WithBot.{0} Nat} {f : Polynomial.{u1} R _inst_1}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) f (Polynomial.degreeLE.{u1} R _inst_1 n)) (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 f) n)
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_degree_le Polynomial.mem_degreeLEₓ'. -/
 theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degree f ≤ n := by
   simp only [degree_le, Submodule.mem_iInf, degree_le_iff_coeff_zero, LinearMap.mem_ker] <;> rfl
 #align polynomial.mem_degree_le Polynomial.mem_degreeLE
--/
 
 /- warning: polynomial.degree_le_mono -> Polynomial.degreeLE_mono is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLE.{u1} R _inst_1 m) (Polynomial.degreeLE.{u1} R _inst_1 n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLE.{u1} R _inst_1 m) (Polynomial.degreeLE.{u1} R _inst_1 n))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLE.{u1} R _inst_1 m) (Polynomial.degreeLE.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_mono Polynomial.degreeLE_monoₓ'. -/
@@ -113,7 +117,12 @@ theorem degreeLE_eq_span_X_pow {n : ℕ} :
 #align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLE_eq_span_X_pow
 -/
 
-#print Polynomial.mem_degreeLT /-
+/- warning: polynomial.mem_degree_lt -> Polynomial.mem_degreeLT is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {f : Polynomial.{u1} R _inst_1}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) f (Polynomial.degreeLT.{u1} R _inst_1 n)) (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 f) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {f : Polynomial.{u1} R _inst_1}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) f (Polynomial.degreeLT.{u1} R _inst_1 n)) (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 f) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) n))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_degree_lt Polynomial.mem_degreeLTₓ'. -/
 theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n :=
   by
   simp_rw [degree_lt, Submodule.mem_iInf, LinearMap.mem_ker, degree, Finset.max_eq_sup_coe,
@@ -121,11 +130,10 @@ theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n
     Ne, not_imp_not]
   rfl
 #align polynomial.mem_degree_lt Polynomial.mem_degreeLT
--/
 
 /- warning: polynomial.degree_lt_mono -> Polynomial.degreeLT_mono is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLT.{u1} R _inst_1 m) (Polynomial.degreeLT.{u1} R _inst_1 n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toHasLe.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLT.{u1} R _inst_1 m) (Polynomial.degreeLT.{u1} R _inst_1 n))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLT.{u1} R _inst_1 m) (Polynomial.degreeLT.{u1} R _inst_1 n))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_mono Polynomial.degreeLT_monoₓ'. -/
@@ -305,12 +313,16 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
 -/
 
-#print Polynomial.Monic.geom_sum' /-
+/- warning: polynomial.monic.geom_sum' -> Polynomial.Monic.geom_sum' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {P : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 P) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R _inst_1 P)) -> (forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Polynomial.Monic.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (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)))) (Finset.range n) (fun (i : Nat) => 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))))) P i))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {P : Polynomial.{u1} R _inst_1}, (Polynomial.Monic.{u1} R _inst_1 P) -> (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R _inst_1 P)) -> (forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Polynomial.Monic.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (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)))) (Finset.range n) (fun (i : Nat) => 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))))) P i))))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.geom_sum' Polynomial.Monic.geom_sum'ₓ'. -/
 theorem Monic.geom_sum' {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.degree) {n : ℕ} (hn : n ≠ 0) :
     (∑ i in range n, P ^ i).Monic :=
   hP.geom_sum (natDegree_pos_iff_degree_pos.2 hdeg) hn
 #align polynomial.monic.geom_sum' Polynomial.Monic.geom_sum'
--/
 
 #print Polynomial.monic_geom_sum_X /-
 theorem monic_geom_sum_X {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (X : R[X]) ^ i).Monic :=
@@ -814,7 +826,7 @@ variable (I : Ideal R[X])
 
 /- warning: ideal.mem_leading_coeff_nth -> Ideal.mem_leadingCoeffNth is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (n : Nat) (x : R), Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n)) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{0} (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) (fun (H : Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) n)) (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) x))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (n : Nat) (x : R), Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n)) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{0} (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) (fun (H : Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) n)) (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) x))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (n : Nat) (x : R), Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n)) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Membership.mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) (And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) n)) (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) x))))
 Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNthₓ'. -/
@@ -859,7 +871,7 @@ theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :
 
 /- warning: ideal.leading_coeff_nth_mono -> Ideal.leadingCoeffNth_mono is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I m) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toHasLe.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I m) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I m) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n))
 Case conversion may be inaccurate. Consider using '#align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_monoₓ'. -/
@@ -1289,7 +1301,7 @@ namespace Polynomial
 
 /- warning: polynomial.exists_irreducible_of_degree_pos -> Polynomial.exists_irreducible_of_degree_pos is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toHasLt.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_degree_pos Polynomial.exists_irreducible_of_degree_posₓ'. -/
@@ -1374,7 +1386,7 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
 
 /- warning: polynomial.sup_ker_aeval_le_ker_aeval_mul -> Polynomial.sup_ker_aeval_le_ker_aeval_mul is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} 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(CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 but is expected to have type
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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_inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mulₓ'. -/

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

@@ -1047,7 +1047,7 @@ theorem isPrime_map_C_of_isPrime {P : Ideal R} (H : IsPrime P) :
 
 #print Ideal.is_fg_degreeLE /-
 theorem is_fg_degreeLE [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
-    Submodule.Fg (I.degreeLE n) :=
+    Submodule.FG (I.degreeLE n) :=
   isNoetherian_submodule_left.1
     (isNoetherian_of_fg_of_noetherian _ ⟨_, degreeLE_eq_span_X_pow.symm⟩) _
 #align ideal.is_fg_degree_le Ideal.is_fg_degreeLE

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -74,7 +74,7 @@ variable {R}
 
 #print Polynomial.mem_degreeLE /-
 theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degree f ≤ n := by
-  simp only [degree_le, Submodule.mem_infᵢ, degree_le_iff_coeff_zero, LinearMap.mem_ker] <;> rfl
+  simp only [degree_le, Submodule.mem_iInf, degree_le_iff_coeff_zero, LinearMap.mem_ker] <;> rfl
 #align polynomial.mem_degree_le Polynomial.mem_degreeLE
 -/
 
@@ -116,7 +116,7 @@ theorem degreeLE_eq_span_X_pow {n : ℕ} :
 #print Polynomial.mem_degreeLT /-
 theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n :=
   by
-  simp_rw [degree_lt, Submodule.mem_infᵢ, LinearMap.mem_ker, degree, Finset.max_eq_sup_coe,
+  simp_rw [degree_lt, Submodule.mem_iInf, LinearMap.mem_ker, degree, Finset.max_eq_sup_coe,
     Finset.sup_lt_iff (WithBot.bot_lt_coe n), mem_support_iff, WithBot.coe_lt_coe, lt_iff_not_le,
     Ne, not_imp_not]
   rfl
@@ -883,7 +883,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff Ideal.mem_leadingCoeffₓ'. -/
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x :=
   by
-  rw [leading_coeff, Submodule.mem_supᵢ_of_directed]
+  rw [leading_coeff, Submodule.mem_iSup_of_directed]
   simp only [mem_leading_coeff_nth]
   · constructor
     · rintro ⟨i, p, hpI, hpdeg, rfl⟩

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

@@ -331,7 +331,7 @@ variable [Ring R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)), Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)), Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)), Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.restriction Polynomial.restrictionₓ'. -/
 /-- Given a polynomial, return the polynomial whose coefficients are in
 the ring closure of the original coefficients. -/
@@ -382,7 +382,7 @@ theorem support_restriction (p : R[X]) : support (restriction p) = support p :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p)))) R (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p)))) (Subring.toRing.{u1} R (CommRing.toRing.{u1} R _inst_2) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (algebraMap.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p)))) R (SubsemiringClass.toCommSemiring.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))) R (CommRing.toCommSemiring.{u1} R _inst_2) (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SubringClass.to_subsemiringClass.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (CommRing.toRing.{u1} R _inst_2) (Subring.setLike.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Subring.subringClass.{u1} R (CommRing.toRing.{u1} R _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Algebra.ofSubring.{u1, u1} R R _inst_2 (CommRing.toRing.{u1} R _inst_2) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Polynomial.restriction.{u1} R (CommRing.toRing.{u1} R _inst_2) p)) p
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2))) (Polynomial.map.{u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) R (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (CommRing.toCommSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Subring.toCommRing.{u1} R _inst_2 (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p)))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (algebraMap.{u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) R (CommRing.toCommSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Subring.toCommRing.{u1} R _inst_2 (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (Algebra.ofSubring.{u1, u1} R R _inst_2 (CommRing.toRing.{u1} R _inst_2) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Polynomial.restriction.{u1} R (CommRing.toRing.{u1} R _inst_2) p)) p
+  forall {R : Type.{u1}} [_inst_2 : CommRing.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2))) (Polynomial.map.{u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) R (CommSemiring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Subsemiring.toCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2) (Subring.toSubsemiring.{u1} R (CommRing.toRing.{u1} R _inst_2) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p)))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (algebraMap.{u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) (SetLike.instMembership.{u1, u1} (Subring.{u1} R (CommRing.toRing.{u1} R _inst_2)) R (Subring.instSetLikeSubring.{u1} R (CommRing.toRing.{u1} R _inst_2))) x (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) R (Subsemiring.toCommSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2) (Subring.toSubsemiring.{u1} R (CommRing.toRing.{u1} R _inst_2) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (Algebra.ofSubring.{u1, u1} R R _inst_2 (CommRing.toRing.{u1} R _inst_2) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_2)) (Subring.closure.{u1} R (CommRing.toRing.{u1} R _inst_2) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_2)) p))))) (Polynomial.restriction.{u1} R (CommRing.toRing.{u1} R _inst_2) p)) p
 Case conversion may be inaccurate. Consider using '#align polynomial.map_restriction Polynomial.map_restrictionₓ'. -/
 @[simp]
 theorem map_restriction {R : Type u} [CommRing R] (p : R[X]) :
@@ -407,7 +407,7 @@ theorem natDegree_restriction {p : R[X]} : (restriction p).natDegree = p.natDegr
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Polynomial.Monic.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Polynomial.restriction.{u1} R _inst_1 p)) (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Polynomial.Monic.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Polynomial.restriction.{u1} R _inst_1 p)) (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Iff (Polynomial.Monic.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) (Polynomial.restriction.{u1} R _inst_1 p)) (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_restriction Polynomial.monic_restrictionₓ'. -/
 @[simp]
 theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
@@ -424,7 +424,7 @@ theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, 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(Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))))) (Polynomial.restriction.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a 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(Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) 0 (OfNat.mk.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) 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(Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) 0 (Zero.zero.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) 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 but is expected to have type
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(Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 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(Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) (Polynomial.restriction.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) (Polynomial.zero.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.restriction_zero Polynomial.restriction_zeroₓ'. -/
 @[simp]
 theorem restriction_zero : restriction (0 : R[X]) = 0 := by
@@ -435,7 +435,7 @@ theorem restriction_zero : restriction (0 : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))))) (Polynomial.restriction.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (OfNat.ofNat.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a 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(Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) 1 (OfNat.mk.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) 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(Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) 1 (One.one.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Polynomial.hasOne.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) (Polynomial.restriction.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) (Polynomial.one.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], Eq.{succ u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) (Polynomial.restriction.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))))) (Polynomial.one.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.restriction_one Polynomial.restriction_oneₓ'. -/
 @[simp]
 theorem restriction_one : restriction (1 : R[X]) = 1 :=
@@ -448,7 +448,7 @@ variable [Semiring S] {f : R →+* S} {x : S}
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : Ring.{u1} R] [_inst_2 : Semiring.{u2} S] {f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)} {x : S} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)}, Eq.{succ u2} S (Polynomial.eval₂.{u1, u2} R S (Ring.toSemiring.{u1} R _inst_1) _inst_2 f x p) (Polynomial.eval₂.{u1, u2} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) S (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) _inst_2 (RingHom.comp.{u1, u1, u2} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) R S (Semiring.toNonAssocSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))) (Subring.toRing.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)))))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2) f (Subring.subtype.{u1} R _inst_1 (Subring.closure.{u1} R _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p))))) x (Polynomial.restriction.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : Semiring.{u1} S] {f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)} {x : S} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) _inst_2 f x p) (Polynomial.eval₂.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) S (Ring.toSemiring.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) (Subring.toRing.{u2} R _inst_1 (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) _inst_2 (RingHom.comp.{u2, u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) R S (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) (Ring.toSemiring.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) (Subring.toRing.{u2} R _inst_1 (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p)))))) (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2) f (Subring.subtype.{u2} R _inst_1 (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) x (Polynomial.restriction.{u2} R _inst_1 p))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : Ring.{u2} R] [_inst_2 : Semiring.{u1} S] {f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)} {x : S} {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R _inst_1)}, Eq.{succ u1} S (Polynomial.eval₂.{u2, u1} R S (Ring.toSemiring.{u2} R _inst_1) _inst_2 f x p) (Polynomial.eval₂.{u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) S (Subsemiring.toSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1) (Subring.toSubsemiring.{u2} R _inst_1 (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) _inst_2 (RingHom.comp.{u2, u2, u1} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) R S (Semiring.toNonAssocSemiring.{u2} (Subtype.{succ u2} R (fun (x : R) => Membership.mem.{u2, u2} R (Subring.{u2} R _inst_1) (SetLike.instMembership.{u2, u2} (Subring.{u2} R _inst_1) R (Subring.instSetLikeSubring.{u2} R _inst_1)) x (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) (Subsemiring.toSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1) (Subring.toSubsemiring.{u2} R _inst_1 (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p)))))) (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2) f (Subring.subtype.{u2} R _inst_1 (Subring.closure.{u2} R _inst_1 (Finset.toSet.{u2} R (Polynomial.frange.{u2} R (Ring.toSemiring.{u2} R _inst_1) p))))) x (Polynomial.restriction.{u2} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_restriction Polynomial.eval₂_restrictionₓ'. -/
 theorem eval₂_restriction {p : R[X]} :
     eval₂ f x p =
@@ -466,7 +466,7 @@ variable (p : R[X]) (T : Subring R)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1), (HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) -> (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1), (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) -> (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1), (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) -> (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_subring Polynomial.toSubringₓ'. -/
 /-- Given a polynomial `p` and a subring `T` that contains the coefficients of `p`,
 return the corresponding polynomial whose coefficients are in `T`. -/
@@ -485,7 +485,7 @@ include hp
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) {n : Nat}, Eq.{succ u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.hasMem.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) x T))))) (Polynomial.coeff.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) {n : Nat}, Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Polynomial.coeff.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) {n : Nat}, Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Polynomial.coeff.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_to_subring Polynomial.coeff_toSubringₓ'. -/
 @[simp]
 theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n :=
@@ -502,7 +502,7 @@ theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) {n : Nat}, Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.hasMem.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) x T) (Polynomial.coeff.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) {n : Nat}, Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T) (Polynomial.coeff.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) {n : Nat}, Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T) (Polynomial.coeff.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_to_subring' Polynomial.coeff_toSubring'ₓ'. -/
 @[simp]
 theorem coeff_toSubring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
@@ -513,7 +513,7 @@ theorem coeff_toSubring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)), Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.support_to_subring Polynomial.support_toSubringₓ'. -/
 @[simp]
 theorem support_toSubring : support (toSubring p T hp) = support p :=
@@ -531,7 +531,7 @@ theorem support_toSubring : support (toSubring p T hp) = support p :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_to_subring Polynomial.degree_toSubringₓ'. -/
 @[simp]
 theorem degree_toSubring : (toSubring p T hp).degree = p.degree := by simp [degree]
@@ -541,7 +541,7 @@ theorem degree_toSubring : (toSubring p T hp).degree = p.degree := by simp [degr
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)), Eq.{1} Nat (Polynomial.natDegree.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{1} Nat (Polynomial.natDegree.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{1} Nat (Polynomial.natDegree.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_to_subring Polynomial.natDegree_toSubringₓ'. -/
 @[simp]
 theorem natDegree_toSubring : (toSubring p T hp).natDegree = p.natDegree := by simp [nat_degree]
@@ -551,7 +551,7 @@ theorem natDegree_toSubring : (toSubring p T hp).natDegree = p.natDegree := by s
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)), Iff (Polynomial.Monic.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Iff (Polynomial.Monic.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Iff (Polynomial.Monic.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.monic_to_subring Polynomial.monic_toSubringₓ'. -/
 @[simp]
 theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
@@ -569,7 +569,7 @@ omit hp
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.toSubring.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) T (Eq.mpr.{0} (HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) True) (Eq.trans.{1} Prop (HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.hasEmptyc.{u1} R)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) True ((fun [self : HasSubset.{u1} (Set.{u1} R)] (ᾰ : Set.{u1} R) (ᾰ_1 : Set.{u1} R) (e_2 : Eq.{succ u1} (Set.{u1} R) ᾰ ᾰ_1) (ᾰ_2 : Set.{u1} R) (ᾰ_3 : Set.{u1} R) (e_3 : Eq.{succ u1} (Set.{u1} R) ᾰ_2 ᾰ_3) => congr.{succ u1, 1} (Set.{u1} R) Prop (HasSubset.Subset.{u1} (Set.{u1} R) self ᾰ) (HasSubset.Subset.{u1} (Set.{u1} R) self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{succ u1, succ u1} (Set.{u1} R) ((Set.{u1} R) -> Prop) ᾰ ᾰ_1 (HasSubset.Subset.{u1} (Set.{u1} R) self) e_2) e_3) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.hasEmptyc.{u1} R)) (Eq.trans.{succ u1} (Set.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.hasEmptyc.{u1} R))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.hasEmptyc.{u1} R)) ((fun [_inst_1 : HasLiftT.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R)] (ᾰ : Finset.{u1} R) (ᾰ_1 : Finset.{u1} R) (e_2 : Eq.{succ u1} (Finset.{u1} R) ᾰ ᾰ_1) => congr_arg.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) ᾰ ᾰ_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) _inst_1) e_2) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.hasEmptyc.{u1} R)) (Polynomial.frange_zero.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Finset.coe_empty.{u1} R)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T) (rfl.{succ u1} (Set.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T))) (propext (HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.hasEmptyc.{u1} R)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) True ((fun {α : Type.{u1}} (s : Set.{u1} α) => iff_true_intro (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α)) s) (Set.empty_subset.{u1} α s)) R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T))))) trivial)) (OfNat.ofNat.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) 0 (OfNat.mk.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) 0 (Zero.zero.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.zero.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.toSubring.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) T (of_eq_true (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Eq.trans.{1} Prop (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.instEmptyCollectionSet.{u1} R)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) True (congrFun.{succ u1, 1} (Set.{u1} R) (fun (a._@.Std.Classes.SetNotation._hyg.7 : Set.{u1} R) => Prop) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R)))) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.instEmptyCollectionSet.{u1} R))) (congrArg.{succ u1, succ u1} (Set.{u1} R) ((Set.{u1} R) -> Prop) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.instEmptyCollectionSet.{u1} R)) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R)) (Finset.coe_empty.{u1} R)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Mathlib.Data.Set.Basic._auxLemma.9.{u1} R (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T))))) (OfNat.ofNat.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.zero.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) (Polynomial.toSubring.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) T (of_eq_true (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Eq.trans.{1} Prop (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.instEmptyCollectionSet.{u1} R)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) True (congrFun.{succ u1, 1} (Set.{u1} R) (fun (a._@.Std.Classes.SetNotation._hyg.7 : Set.{u1} R) => Prop) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R)))) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.instEmptyCollectionSet.{u1} R))) (congrArg.{succ u1, succ u1} (Set.{u1} R) ((Set.{u1} R) -> Prop) (Finset.toSet.{u1} R (EmptyCollection.emptyCollection.{u1} (Finset.{u1} R) (Finset.instEmptyCollectionFinset.{u1} R))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} R) (Set.instEmptyCollectionSet.{u1} R)) (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R)) (Finset.coe_empty.{u1} R)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Mathlib.Data.Set.Basic._auxLemma.9.{u1} R (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T))))) (OfNat.ofNat.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) (Polynomial.zero.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_subring_zero Polynomial.toSubring_zeroₓ'. -/
 @[simp]
 theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 :=
@@ -582,7 +582,7 @@ theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.toSubring.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) T (Set.Subset.trans.{u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.one.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.hasOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (fun (x : R) => Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Finset.val.{u1} R (Singleton.singleton.{u1, u1} R (Finset.{u1} R) (Finset.hasSingleton.{u1} R) (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 (Ring.toSemiring.{u1} R _inst_1))))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T) (Polynomial.frange_one.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Iff.mpr (HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Singleton.singleton.{u1, u1} R (Finset.{u1} R) (Finset.hasSingleton.{u1} R) (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 (Ring.toSemiring.{u1} R _inst_1)))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) (Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) (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 (Ring.toSemiring.{u1} R _inst_1)))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) (Finset.singleton_subset_set_iff.{u1} R ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T) (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 (Ring.toSemiring.{u1} R _inst_1))))))))) (Subring.one_mem.{u1} R _inst_1 T)))) (OfNat.ofNat.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) 1 (OfNat.mk.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) 1 (One.one.{u1} (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.hasOne.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.toSubring.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) T (Set.Subset.trans.{u1} R (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (fun (x : R) => Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Finset.val.{u1} R (Singleton.singleton.{u1, u1} R (Finset.{u1} R) (Finset.instSingletonFinset.{u1} R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T) (Polynomial.frange_one.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Iff.mpr (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Singleton.singleton.{u1, u1} R (Finset.{u1} R) (Finset.instSingletonFinset.{u1} R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Finset.singleton_subset_set_iff.{u1} R (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Subring.one_mem.{u1} R _inst_1 T)))) (OfNat.ofNat.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) (Polynomial.one.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)))))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) (Polynomial.toSubring.{u1} R _inst_1 (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) T (Set.Subset.trans.{u1} R (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.one.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (fun (x : R) => Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Finset.val.{u1} R (Singleton.singleton.{u1, u1} R (Finset.{u1} R) (Finset.instSingletonFinset.{u1} R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T) (Polynomial.frange_one.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Iff.mpr (HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Singleton.singleton.{u1, u1} R (Finset.{u1} R) (Finset.instSingletonFinset.{u1} R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Finset.singleton_subset_set_iff.{u1} R (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Subring.one_mem.{u1} R _inst_1 T)))) (OfNat.ofNat.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) 1 (One.toOfNat1.{u1} (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) (Polynomial.one.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.to_subring_one Polynomial.toSubring_oneₓ'. -/
 @[simp]
 theorem toSubring_one :
@@ -596,7 +596,7 @@ theorem toSubring_one :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.map.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Ring.toSemiring.{u1} R _inst_1) (Subring.subtype.{u1} R _inst_1 T) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) p
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.map.{u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) R (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Ring.toSemiring.{u1} R _inst_1) (Subring.subtype.{u1} R _inst_1 T) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) p
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.map.{u1, u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) R (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) (Ring.toSemiring.{u1} R _inst_1) (Subring.subtype.{u1} R _inst_1 T) (Polynomial.toSubring.{u1} R _inst_1 p T hp)) p
 Case conversion may be inaccurate. Consider using '#align polynomial.map_to_subring Polynomial.map_toSubringₓ'. -/
 @[simp]
 theorem map_toSubring : (p.toSubring T hp).map (Subring.subtype T) = p :=
@@ -613,7 +613,7 @@ variable (T : Subring R)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), (Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1), (Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1))
 Case conversion may be inaccurate. Consider using '#align polynomial.of_subring Polynomial.ofSubringₓ'. -/
 /-- Given a polynomial whose coefficients are in some subring, return
 the corresponding polynomial whose coefficients are in the ambient ring. -/
@@ -625,7 +625,7 @@ def ofSubring (p : T[X]) : R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1) (p : Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Polynomial.ofSubring.{u1} R _inst_1 T p) n) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) R (coeSubtype.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.hasMem.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) x T))))) (Polynomial.coeff.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) p n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1) (p : Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Polynomial.ofSubring.{u1} R _inst_1 T p) n) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Polynomial.coeff.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) p n))
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1) (p : Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Polynomial.ofSubring.{u1} R _inst_1 T p) n) (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) x (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) (Polynomial.coeff.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T)) p n))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_of_subring Polynomial.coeff_ofSubringₓ'. -/
 theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff p n : T) :=
   by
@@ -640,7 +640,7 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1) {p : Polynomial.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T))}, HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Polynomial.ofSubring.{u1} R _inst_1 T p))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1) {p : Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T))}, HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Polynomial.ofSubring.{u1} R _inst_1 T p))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (T : Subring.{u1} R _inst_1) {p : Polynomial.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subsemiring.toSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Subring.toSubsemiring.{u1} R _inst_1 T))}, HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) (Polynomial.ofSubring.{u1} R _inst_1 T p))) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)
 Case conversion may be inaccurate. Consider using '#align polynomial.frange_of_subring Polynomial.frange_ofSubringₓ'. -/
 @[simp]
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T :=
@@ -666,7 +666,7 @@ variable {q : R[X]}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) p (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q))) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) q p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) p (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q))) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) q p))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q) -> (forall {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) p (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q))) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) q p))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monicₓ'. -/
 theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q).ker ↔ q ∣ p :=
   LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
@@ -676,7 +676,7 @@ theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Eq.{succ u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.smulZeroClass.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Polynomial.isScalarTower_right.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSingleton.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) q))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Eq.{succ u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.isScalarTower_right.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) q))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) q) -> (Eq.{succ u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.isScalarTower_right.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) q))))
 Case conversion may be inaccurate. Consider using '#align polynomial.ker_mod_by_monic_hom Polynomial.ker_modByMonicHomₓ'. -/
 @[simp]
 theorem ker_modByMonicHom (hq : q.Monic) :
@@ -972,7 +972,7 @@ variable [CommRing R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Iff (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P)) (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Iff (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P)) (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (P : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), Iff (Ideal.IsPrime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) P)) (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) P)
 Case conversion may be inaccurate. Consider using '#align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrimeₓ'. -/
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
@@ -1037,7 +1037,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P) -> (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P) -> (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {P : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) P) -> (Ideal.IsPrime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) P))
 Case conversion may be inaccurate. Consider using '#align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrimeₓ'. -/
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_of_isPrime {P : Ideal R} (H : IsPrime P) :
@@ -1071,7 +1071,7 @@ namespace Polynomial
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r) (Polynomial.commRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r) (Polynomial.commRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
 Case conversion may be inaccurate. Consider using '#align polynomial.prime_C_iff Polynomial.prime_C_iffₓ'. -/
 theorem prime_C_iff : Prime (C r) ↔ Prime r :=
   ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr =>
@@ -1291,7 +1291,7 @@ namespace Polynomial
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_degree_pos Polynomial.exists_irreducible_of_degree_posₓ'. -/
 theorem exists_irreducible_of_degree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.degree) : ∃ g, Irreducible g ∧ g ∣ f :=
@@ -1303,7 +1303,7 @@ theorem exists_irreducible_of_degree_pos {R : Type u} [CommRing R] [IsDomain R]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_nat_degree_pos Polynomial.exists_irreducible_of_natDegree_posₓ'. -/
 theorem exists_irreducible_of_natDegree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.natDegree) : ∃ g, Irreducible g ∧ g ∣ f :=
@@ -1316,7 +1316,7 @@ theorem exists_irreducible_of_natDegree_pos {R : Type u} [CommRing R] [IsDomain
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5)) f) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
 Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zeroₓ'. -/
 theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDomain R]
     [WfDvdMonoid R] {f : R[X]} (hf : f.natDegree ≠ 0) : ∃ g, Irreducible g ∧ g ∣ f :=
@@ -1327,7 +1327,7 @@ theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDom
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R M (fun (n : Nat) => coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) f n) v) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (forall (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Eq.{succ u2} M (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => M -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (AddCommGroup.toAddGroup.{u2} M _inst_3))))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (OfNat.mk.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.zero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (fun (n : Nat) => FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.monoid.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) f n) v) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) _inst_3) _inst_4) (forall (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) _inst_3)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (v : M), Iff (LinearIndependent.{0, u1, u2} Nat R ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (fun (n : Nat) => FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u2, 0, u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (Monoid.Pow.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.monoid.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) f n) v) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) _inst_3) _inst_4) (forall (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))), (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (FunLike.coe.{succ u2, succ u2, succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R 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(CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) 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(Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p) v) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (NegZeroClass.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubNegZeroMonoid.toNegZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubtractionMonoid.toSubNegZeroMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (SubtractionCommMonoid.toSubtractionMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) (AddCommGroup.toDivisionAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => M) v) _inst_3)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) p (OfNat.ofNat.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.zero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aevalₓ'. -/
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 :=
@@ -1355,7 +1355,7 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) p)) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.hasTop.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
 but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) 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_inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R 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_inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.range.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R 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R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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_inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) q))) (Top.top.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.instTopSubmodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprimeₓ'. -/
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=
@@ -1376,7 +1376,7 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SetLike.partialOrder.{u2, u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) M (Submodule.setLike.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} 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(CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M 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(Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.End.algebra.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 but is expected to have type
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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) 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_inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R 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_inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R 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_inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, 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(CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p q)))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] {f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, LE.le.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Preorder.toLE.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R 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(AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R 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_inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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(CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) 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(CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R 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R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q)))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mulₓ'. -/
 theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     (aeval f p).ker ⊔ (aeval f q).ker ≤ (aeval f (p * q)).ker :=
@@ -1394,7 +1394,7 @@ theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
 lean 3 declaration is
   forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) 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(Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R 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(DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p q))))
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {q : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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(Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M 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_inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R 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(RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R 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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (Polynomial.aeval.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
 Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprimeₓ'. -/
 theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X]}
     (hpq : IsCoprime p q) : (aeval f p).ker ⊔ (aeval f q).ker = (aeval f (p * q)).ker :=
@@ -1527,7 +1527,7 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] : IsDomain (MvPoly
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {S : Type.{u3}} [_inst_5 : CommRing.{u3} S] [_inst_6 : Finite.{succ u2} σ] (ϕ : RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) (p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)), Eq.{succ u3} S (coeFn.{max (succ (max u2 u1)) (succ u3), max (succ (max u2 u1)) (succ u3)} (RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) (fun (_x : RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> S) (RingHom.hasCoeToFun.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) ϕ p) (MvPolynomial.eval₂.{u1, u3, u2} R S σ (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u3} S _inst_5) (RingHom.comp.{u1, max u2 u1, u3} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5))) ϕ (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (s : σ) => coeFn.{max (succ (max u2 u1)) (succ u3), max (succ (max u2 u1)) (succ u3)} (RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) (fun (_x : RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> S) (RingHom.hasCoeToFun.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) ϕ (MvPolynomial.X.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) s)) p)
 but is expected to have type
-  forall {R : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_5 : CommRing.{u1} S] [_inst_6 : Finite.{succ u3} σ] (ϕ : RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) p) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) 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(MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))))) ϕ p) (MvPolynomial.eval₂.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} S _inst_5) (RingHom.comp.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) ϕ (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (s : σ) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 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R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))))) ϕ (MvPolynomial.X.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s)) p)
+  forall {R : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_5 : CommRing.{u1} S] [_inst_6 : Finite.{succ u3} σ] (ϕ : RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) p) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, u1} 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(CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) ϕ p) (MvPolynomial.eval₂.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} S _inst_5) (RingHom.comp.{u2, max u2 u3, u1} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) ϕ (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (s : σ) => FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u2) (succ u3), succ u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (fun (_x : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonUnitalNonAssocSemiring.toMul.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) ϕ (MvPolynomial.X.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s)) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂ₓ'. -/
 theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :
@@ -1545,7 +1545,7 @@ theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ :
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)), (forall (m : Finsupp.{u2, 0} σ Nat Nat.hasZero), Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m p) (Ideal.comap.{u1, max u2 u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (RingHom.ringHomClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) -> (Membership.Mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) p I)
 but is expected to have type
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)), (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m p) (Ideal.comap.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) -> (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) p I)
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)), (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m p) (Ideal.comap.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) -> (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) p I)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_ideal_of_coeff_mem_ideal MvPolynomial.mem_ideal_of_coeff_mem_idealₓ'. -/
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself,
 multivariate version. -/
@@ -1565,7 +1565,7 @@ theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPoly
 lean 3 declaration is
   forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Membership.Mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) f (Ideal.map.{u1, max u2 u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (RingHom.ringHomClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) (forall (m : Finsupp.{u2, 0} σ Nat Nat.hasZero), Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m f) I)
 but is expected to have type
-  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) f (Ideal.map.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m f) I)
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {f : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) f (Ideal.map.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m f) I)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_C_iffₓ'. -/
 /-- The push-forward of an ideal `I` of `R` to `mv_polynomial σ R` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
@@ -1603,7 +1603,7 @@ theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u3} S] (f : RingHom.{u1, u3} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))), Eq.{succ (max u2 u1)} (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.ker.{max u2 u1, max u2 u3, max (max u2 u1) u2 u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (RingHom.{max u2 u1, max u2 u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (MvPolynomial.commSemiring.{u3, u2} S σ (CommRing.toCommSemiring.{u3} S _inst_2))))) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (MvPolynomial.commSemiring.{u3, u2} S σ (CommRing.toCommSemiring.{u3} S _inst_2))) (RingHom.ringHomClass.{max u2 u1, max u2 u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (MvPolynomial.commSemiring.{u3, u2} S σ (CommRing.toCommSemiring.{u3} S _inst_2))))) (MvPolynomial.map.{u1, u3, u2} R S σ (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u3} S _inst_2) f)) (Ideal.map.{u1, max u2 u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.ker.{u1, u3, max u1 u3} R S (RingHom.{u1, u3} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) (RingHom.ringHomClass.{u1, u3} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) f))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))), Eq.{max (succ u2) (succ u3)} (Ideal.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u2 u3, max u3 u1, max (max u2 u3) u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u3, max u3 u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))))) (MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} S _inst_2) f)) (Ideal.map.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.ker.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) f))
+  forall {R : Type.{u2}} {S : Type.{u1}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))), Eq.{max (succ u2) (succ u3)} (Ideal.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u2 u3, max u3 u1, max (max u2 u3) u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u3, max u3 u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))))) (MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} S _inst_2) f)) (Ideal.map.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.ker.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) f))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.ker_map MvPolynomial.ker_mapₓ'. -/
 theorem ker_map (f : R →+* S) :
     (map f : MvPolynomial σ R →+* MvPolynomial σ S).ker = f.ker.map (C : R →+* MvPolynomial σ R) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

@@ -676,7 +676,7 @@ theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Eq.{succ u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (SMulZeroClass.toHasSmul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.zero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.smulZeroClass.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))))) (Polynomial.isScalarTower_right.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSingleton.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) q))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Eq.{succ u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_1 (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.isScalarTower_right.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_1 (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) q))))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Eq.{succ u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.isScalarTower_right.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) q))))
 Case conversion may be inaccurate. Consider using '#align polynomial.ker_mod_by_monic_hom Polynomial.ker_modByMonicHomₓ'. -/
 @[simp]
 theorem ker_modByMonicHom (hq : q.Monic) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

@@ -198,7 +198,7 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((Fin n) -> R) (coeFn.{succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.Function.module.{0, u1, u1} (Fin n) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 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NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.Function.module.{0, u1, u1} (Fin n) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (OfNat.ofNat.{u1} ((Fin n) -> R) 0 (OfNat.mk.{u1} ((Fin n) -> R) 0 (Zero.zero.{u1} ((Fin n) -> R) (Pi.instZero.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (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
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(Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (fun (_x : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x 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_inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (SMulZeroClass.toSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, 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((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) 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(a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (Pi.instZero.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) 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u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} 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Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (Pi.instZero.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zeroₓ'. -/
 @[simp]
 theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) :
@@ -210,7 +210,7 @@ theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degre
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Finset.sum.{u1, 0} R (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.Function.module.{0, u1, u1} (Fin n) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R 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(Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i))))
 but is expected to have type
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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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R 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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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 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_inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R 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_inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} 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(Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 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R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (Fin.val n i))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Finset.sum.{u1, 0} R (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R 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_inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R 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R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1055 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, 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_inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (Fin.val n i))))
 Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquivₓ'. -/
 theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
     p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
@@ -498,16 +498,16 @@ theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n
   · rfl
 #align polynomial.coeff_to_subring Polynomial.coeff_toSubring
 
-/- warning: polynomial.coeff_to_subring' -> Polynomial.coeff_to_subring' is a dubious translation:
+/- warning: polynomial.coeff_to_subring' -> Polynomial.coeff_toSubring' is a dubious translation:
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.hasSubset.{u1} R) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} R) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} R) (Set.{u1} R) (Finset.Set.hasCoeT.{u1} R))) (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Subring.{u1} R _inst_1) (Set.{u1} R) (HasLiftT.mk.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (CoeTCₓ.coe.{succ u1, succ u1} (Subring.{u1} R _inst_1) (Set.{u1} R) (SetLike.Set.hasCoeT.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)))) T)) {n : Nat}, Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.Mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.hasMem.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) x T) (Polynomial.coeff.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Ring.toSemiring.{u1} (coeSort.{succ u1, succ (succ u1)} (Subring.{u1} R _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.setLike.{u1} R _inst_1)) T) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (T : Subring.{u1} R _inst_1) (hp : HasSubset.Subset.{u1} (Set.{u1} R) (Set.instHasSubsetSet.{u1} R) (Finset.toSet.{u1} R (Polynomial.frange.{u1} R (Ring.toSemiring.{u1} R _inst_1) p)) (SetLike.coe.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1) T)) {n : Nat}, Eq.{succ u1} R (Subtype.val.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T) (Polynomial.coeff.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Ring.toSemiring.{u1} (Subtype.{succ u1} R (fun (x : R) => Membership.mem.{u1, u1} R (Subring.{u1} R _inst_1) (SetLike.instMembership.{u1, u1} (Subring.{u1} R _inst_1) R (Subring.instSetLikeSubring.{u1} R _inst_1)) x T)) (Subring.toRing.{u1} R _inst_1 T)) (Polynomial.toSubring.{u1} R _inst_1 p T hp) n)) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R _inst_1) p n)
-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_to_subring' Polynomial.coeff_to_subring'ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_to_subring' Polynomial.coeff_toSubring'ₓ'. -/
 @[simp]
-theorem coeff_to_subring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
+theorem coeff_toSubring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
   coeff_toSubring _ _ hp
-#align polynomial.coeff_to_subring' Polynomial.coeff_to_subring'
+#align polynomial.coeff_to_subring' Polynomial.coeff_toSubring'
 
 /- warning: polynomial.support_to_subring -> Polynomial.support_toSubring is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.basic
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.RingTheory.UniqueFactorizationDomain
 /-!
 # Ring-theoretic supplement of data.polynomial.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main results
 * `mv_polynomial.is_domain`:
   If a ring is an integral domain, then so is its polynomial ring over finitely many variables.

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

@@ -53,42 +53,42 @@ instance (p : ℕ) [h : CharP R p] : CharP R[X] p :=
 
 variable (R)
 
-#print Polynomial.degreeLe /-
+#print Polynomial.degreeLE /-
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree ≤ `n`. -/
-def degreeLe (n : WithBot ℕ) : Submodule R R[X] :=
+def degreeLE (n : WithBot ℕ) : Submodule R R[X] :=
   ⨅ k : ℕ, ⨅ h : ↑k > n, (lcoeff R k).ker
-#align polynomial.degree_le Polynomial.degreeLe
+#align polynomial.degree_le Polynomial.degreeLE
 -/
 
-#print Polynomial.degreeLt /-
+#print Polynomial.degreeLT /-
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree < `n`. -/
-def degreeLt (n : ℕ) : Submodule R R[X] :=
+def degreeLT (n : ℕ) : Submodule R R[X] :=
   ⨅ k : ℕ, ⨅ h : k ≥ n, (lcoeff R k).ker
-#align polynomial.degree_lt Polynomial.degreeLt
+#align polynomial.degree_lt Polynomial.degreeLT
 -/
 
 variable {R}
 
-#print Polynomial.mem_degreeLe /-
-theorem mem_degreeLe {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLe R n ↔ degree f ≤ n := by
+#print Polynomial.mem_degreeLE /-
+theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degree f ≤ n := by
   simp only [degree_le, Submodule.mem_infᵢ, degree_le_iff_coeff_zero, LinearMap.mem_ker] <;> rfl
-#align polynomial.mem_degree_le Polynomial.mem_degreeLe
+#align polynomial.mem_degree_le Polynomial.mem_degreeLE
 -/
 
-/- warning: polynomial.degree_le_mono -> Polynomial.degreeLe_mono is a dubious translation:
+/- warning: polynomial.degree_le_mono -> Polynomial.degreeLE_mono is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLe.{u1} R _inst_1 m) (Polynomial.degreeLe.{u1} R _inst_1 n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLE.{u1} R _inst_1 m) (Polynomial.degreeLE.{u1} R _inst_1 n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLe.{u1} R _inst_1 m) (Polynomial.degreeLe.{u1} R _inst_1 n))
-Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_mono Polynomial.degreeLe_monoₓ'. -/
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLE.{u1} R _inst_1 m) (Polynomial.degreeLE.{u1} R _inst_1 n))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_mono Polynomial.degreeLE_monoₓ'. -/
 @[mono]
-theorem degreeLe_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLe R m ≤ degreeLe R n := fun f hf =>
-  mem_degreeLe.2 (le_trans (mem_degreeLe.1 hf) H)
-#align polynomial.degree_le_mono Polynomial.degreeLe_mono
+theorem degreeLE_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLE R m ≤ degreeLE R n := fun f hf =>
+  mem_degreeLE.2 (le_trans (mem_degreeLE.1 hf) H)
+#align polynomial.degree_le_mono Polynomial.degreeLE_mono
 
-#print Polynomial.degreeLe_eq_span_X_pow /-
-theorem degreeLe_eq_span_X_pow {n : ℕ} :
-    degreeLe R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) :=
+#print Polynomial.degreeLE_eq_span_X_pow /-
+theorem degreeLE_eq_span_X_pow {n : ℕ} :
+    degreeLE R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) :=
   by
   apply le_antisymm
   · intro p hp
@@ -107,33 +107,33 @@ theorem degreeLe_eq_span_X_pow {n : ℕ} :
   intro k hk; apply mem_degree_le.2
   exact
     (degree_X_pow_le _).trans (WithBot.coe_le_coe.2 <| Nat.le_of_lt_succ <| Finset.mem_range.1 hk)
-#align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLe_eq_span_X_pow
+#align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLE_eq_span_X_pow
 -/
 
-#print Polynomial.mem_degreeLt /-
-theorem mem_degreeLt {n : ℕ} {f : R[X]} : f ∈ degreeLt R n ↔ degree f < n :=
+#print Polynomial.mem_degreeLT /-
+theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n :=
   by
   simp_rw [degree_lt, Submodule.mem_infᵢ, LinearMap.mem_ker, degree, Finset.max_eq_sup_coe,
     Finset.sup_lt_iff (WithBot.bot_lt_coe n), mem_support_iff, WithBot.coe_lt_coe, lt_iff_not_le,
     Ne, not_imp_not]
   rfl
-#align polynomial.mem_degree_lt Polynomial.mem_degreeLt
+#align polynomial.mem_degree_lt Polynomial.mem_degreeLT
 -/
 
-/- warning: polynomial.degree_lt_mono -> Polynomial.degreeLt_mono is a dubious translation:
+/- warning: polynomial.degree_lt_mono -> Polynomial.degreeLT_mono is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLt.{u1} R _inst_1 m) (Polynomial.degreeLt.{u1} R _inst_1 n))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLT.{u1} R _inst_1 m) (Polynomial.degreeLT.{u1} R _inst_1 n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLt.{u1} R _inst_1 m) (Polynomial.degreeLt.{u1} R _inst_1 n))
-Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_mono Polynomial.degreeLt_monoₓ'. -/
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLT.{u1} R _inst_1 m) (Polynomial.degreeLT.{u1} R _inst_1 n))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_mono Polynomial.degreeLT_monoₓ'. -/
 @[mono]
-theorem degreeLt_mono {m n : ℕ} (H : m ≤ n) : degreeLt R m ≤ degreeLt R n := fun f hf =>
-  mem_degreeLt.2 (lt_of_lt_of_le (mem_degreeLt.1 hf) <| WithBot.coe_le_coe.2 H)
-#align polynomial.degree_lt_mono Polynomial.degreeLt_mono
+theorem degreeLT_mono {m n : ℕ} (H : m ≤ n) : degreeLT R m ≤ degreeLT R n := fun f hf =>
+  mem_degreeLT.2 (lt_of_lt_of_le (mem_degreeLT.1 hf) <| WithBot.coe_le_coe.2 H)
+#align polynomial.degree_lt_mono Polynomial.degreeLT_mono
 
-#print Polynomial.degreeLt_eq_span_X_pow /-
-theorem degreeLt_eq_span_X_pow {n : ℕ} :
-    degreeLt R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) :=
+#print Polynomial.degreeLT_eq_span_X_pow /-
+theorem degreeLT_eq_span_X_pow {n : ℕ} :
+    degreeLT R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) :=
   by
   apply le_antisymm
   · intro p hp
@@ -150,18 +150,18 @@ theorem degreeLt_eq_span_X_pow {n : ℕ} :
   rw [Submodule.span_le, Finset.coe_image, Set.image_subset_iff]
   intro k hk; apply mem_degree_lt.2
   exact lt_of_le_of_lt (degree_X_pow_le _) (WithBot.coe_lt_coe.2 <| Finset.mem_range.1 hk)
-#align polynomial.degree_lt_eq_span_X_pow Polynomial.degreeLt_eq_span_X_pow
+#align polynomial.degree_lt_eq_span_X_pow Polynomial.degreeLT_eq_span_X_pow
 -/
 
-#print Polynomial.degreeLtEquiv /-
+#print Polynomial.degreeLTEquiv /-
 /-- The first `n` coefficients on `degree_lt n` form a linear equivalence with `fin n → R`. -/
-def degreeLtEquiv (R) [Semiring R] (n : ℕ) : degreeLt R n ≃ₗ[R] Fin n → R
+def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n → R
     where
   toFun p n := (↑p : R[X]).coeff n
   invFun f :=
     ⟨∑ i : Fin n, monomial i (f i),
-      (degreeLt R n).sum_mem fun i _ =>
-        mem_degreeLt.mpr
+      (degreeLT R n).sum_mem fun i _ =>
+        mem_degreeLT.mpr
           (lt_of_le_of_lt (degree_monomial_le i (f i)) (WithBot.coe_lt_coe.mpr i.is_lt))⟩
   map_add' p q := by
     ext
@@ -188,33 +188,33 @@ def degreeLtEquiv (R) [Semiring R] (n : ℕ) : degreeLt R n ≃ₗ[R] Fin n →
       rwa [← Fin.ext_iff]
     · intro h
       exact (h (Finset.mem_univ _)).elim
-#align polynomial.degree_lt_equiv Polynomial.degreeLtEquiv
+#align polynomial.degree_lt_equiv Polynomial.degreeLTEquiv
 -/
 
-/- warning: polynomial.degree_lt_equiv_eq_zero_iff_eq_zero -> Polynomial.degreeLtEquiv_eq_zero_iff_eq_zero is a dubious translation:
+/- warning: polynomial.degree_lt_equiv_eq_zero_iff_eq_zero -> Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLt.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((Fin n) -> R) (coeFn.{succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLt.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) 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(RingHomInvPair.ids.{u1} R _inst_1)) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (OfNat.ofNat.{u1} ((Fin n) -> R) 0 (OfNat.mk.{u1} ((Fin n) -> R) 0 (Zero.zero.{u1} ((Fin n) -> R) (Pi.instZero.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (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 : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLt.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R 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_inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))) 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_inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R 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(Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, 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n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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_inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n)) p hp)) (Pi.instZero.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
-Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLtEquiv_eq_zero_iff_eq_zeroₓ'. -/
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (fun (_x : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 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_inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) 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(Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) 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((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zeroₓ'. -/
 @[simp]
-theorem degreeLtEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n) :
-    degreeLtEquiv _ _ ⟨p, hp⟩ = 0 ↔ p = 0 := by
+theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) :
+    degreeLTEquiv _ _ ⟨p, hp⟩ = 0 ↔ p = 0 := by
   rw [LinearEquiv.map_eq_zero_iff, Submodule.mk_eq_zero]
-#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLtEquiv_eq_zero_iff_eq_zero
+#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero
 
-/- warning: polynomial.eval_eq_sum_degree_lt_equiv -> Polynomial.eval_eq_sum_degreeLtEquiv is a dubious translation:
+/- warning: polynomial.eval_eq_sum_degree_lt_equiv -> Polynomial.eval_eq_sum_degreeLTEquiv is a dubious translation:
 lean 3 declaration is
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succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLt.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.Function.module.{0, u1, u1} (Fin n) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLt.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R 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(coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLt.{u1} R _inst_1 n)) -> (Fin n) -> R) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLt.{u1} R _inst_1 n)) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.Function.module.{0, u1, u1} (Fin n) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Polynomial.degreeLtEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i))))
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_inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Finset.sum.{u1, 0} R (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, 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_inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R 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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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) -> (Fin n) -> R) (LinearEquiv.hasCoeToFun.{u1, u1, u1, u1} R R (coeSort.{succ u1, succ (succ u1)} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) (Polynomial.degreeLT.{u1} R _inst_1 n)) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) 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(Pi.Function.module.{0, u1, u1} (Fin n) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (Fin n) Nat (HasLiftT.mk.{1, 1} (Fin n) Nat (CoeTCₓ.coe.{1, 1} (Fin n) Nat (coeBase.{1, 1} (Fin n) Nat (Fin.coeToNat n)))) i))))
 but is expected to have type
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(Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) 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(Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R 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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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u1, u1} R R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLtEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (Fin.val n i))))
-Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLtEquivₓ'. -/
-theorem eval_eq_sum_degreeLtEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n) (x : R) :
-    p.eval x = ∑ i, degreeLtEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLT.{u1} R _inst_1 n)) (x : R), Eq.{succ u1} R (Polynomial.eval.{u1} R _inst_1 x p) (Finset.sum.{u1, 0} R (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (fun (_x : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) => (Fin n) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (SMulZeroClass.toSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 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(Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R 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(Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (SemilinearMapClass.distribMulActionHomClass.{u1, u1, u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) 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(Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n))) ((Fin n) -> R) _inst_1 _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLT.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (Polynomial.degreeLTEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLT.{u1} R _inst_1 n)) p hp) i) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) x (Fin.val n i))))
+Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquivₓ'. -/
+theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
+    p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
   by
   simp_rw [eval_eq_sum]
   exact (sum_fin _ (by simp_rw [MulZeroClass.zero_mul, forall_const]) (mem_degree_lt.mp hp)).symm
-#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLtEquiv
+#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquiv
 
 #print Polynomial.frange /-
 /-- The finset of nonzero coefficients of a polynomial. -/
@@ -718,19 +718,19 @@ theorem mem_ofPolynomial (x) : x ∈ I.ofPolynomial ↔ x ∈ I :=
 
 variable (I)
 
-#print Ideal.degreeLe /-
+#print Ideal.degreeLE /-
 /-- Given an ideal `I` of `R[X]`, make the `R`-submodule of `I`
 consisting of polynomials of degree ≤ `n`. -/
-def degreeLe (n : WithBot ℕ) : Submodule R R[X] :=
-  degreeLe R n ⊓ I.ofPolynomial
-#align ideal.degree_le Ideal.degreeLe
+def degreeLE (n : WithBot ℕ) : Submodule R R[X] :=
+  degreeLE R n ⊓ I.ofPolynomial
+#align ideal.degree_le Ideal.degreeLE
 -/
 
 #print Ideal.leadingCoeffNth /-
 /-- Given an ideal `I` of `R[X]`, make the ideal in `R` of
 leading coefficients of polynomials in `I` with degree ≤ `n`. -/
 def leadingCoeffNth (n : ℕ) : Ideal R :=
-  (I.degreeLe n).map <| lcoeff R n
+  (I.degreeLE n).map <| lcoeff R n
 #align ideal.leading_coeff_nth Ideal.leadingCoeffNth
 -/
 
@@ -1042,12 +1042,12 @@ theorem isPrime_map_C_of_isPrime {P : Ideal R} (H : IsPrime P) :
   (isPrime_map_C_iff_isPrime P).mpr H
 #align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrime
 
-#print Ideal.is_fg_degreeLe /-
-theorem is_fg_degreeLe [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
-    Submodule.Fg (I.degreeLe n) :=
+#print Ideal.is_fg_degreeLE /-
+theorem is_fg_degreeLE [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
+    Submodule.Fg (I.degreeLE n) :=
   isNoetherian_submodule_left.1
-    (isNoetherian_of_fg_of_noetherian _ ⟨_, degreeLe_eq_span_X_pow.symm⟩) _
-#align ideal.is_fg_degree_le Ideal.is_fg_degreeLe
+    (isNoetherian_of_fg_of_noetherian _ ⟨_, degreeLE_eq_span_X_pow.symm⟩) _
+#align ideal.is_fg_degree_le Ideal.is_fg_degreeLE
 -/
 
 end CommRing
@@ -1202,21 +1202,21 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
           (Set.range I.leadingCoeffNth) ⟨_, ⟨0, rfl⟩⟩
       have hm : M ∈ Set.range I.leadingCoeffNth := WellFounded.min_mem _ _ _
       let ⟨N, HN⟩ := hm
-      let ⟨s, hs⟩ := I.is_fg_degreeLe N
+      let ⟨s, hs⟩ := I.is_fg_degreeLE N
       have hm2 : ∀ k, I.leadingCoeffNth k ≤ M := fun k =>
         Or.cases_on (le_or_lt k N) (fun h => HN ▸ I.leadingCoeffNth_mono h) fun h x hx =>
           by_contradiction fun hxm =>
             have : ¬M < I.leadingCoeffNth k := by
               refine' WellFounded.not_lt_min (wellFounded_submodule_gt _ _) _ _ _ <;> exact ⟨k, rfl⟩
             this ⟨HN ▸ I.leadingCoeffNth_mono (le_of_lt h), fun H => hxm (H hx)⟩
-      have hs2 : ∀ {x}, x ∈ I.degreeLe N → x ∈ Ideal.span (↑s : Set R[X]) :=
+      have hs2 : ∀ {x}, x ∈ I.degreeLE N → x ∈ Ideal.span (↑s : Set R[X]) :=
         hs ▸ fun x hx =>
           Submodule.span_induction hx (fun _ hx => Ideal.subset_span hx) (Ideal.zero_mem _)
             (fun _ _ => Ideal.add_mem _) fun c f hf => f.C_mul' c ▸ Ideal.mul_mem_left _ _ hf
       ⟨s,
         le_antisymm
             (Ideal.span_le.2 fun x hx =>
-              have : x ∈ I.degreeLe N := hs ▸ Submodule.subset_span hx
+              have : x ∈ I.degreeLE N := hs ▸ Submodule.subset_span hx
               this.2) <|
           by
           have : Submodule.span R[X] ↑s = Ideal.span ↑s := by rfl
@@ -1228,7 +1228,7 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
           · subst k
             refine'
               hs2
-                ⟨Polynomial.mem_degreeLe.2
+                ⟨Polynomial.mem_degreeLE.2
                     (le_trans Polynomial.degree_le_natDegree <| WithBot.coe_le_coe.2 h),
                   hp⟩
           · have hp0 : p ≠ 0 := by
@@ -1276,7 +1276,7 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
                 exact Ideal.zero_mem _
               refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
               rwa [Polynomial.degree_eq_natDegree hpq, WithBot.coe_lt_coe, hn] at this
-            exact hs2 ⟨Polynomial.mem_degreeLe.2 hdq, hq⟩⟩⟩
+            exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
 #align polynomial.is_noetherian_ring Polynomial.isNoetherianRing
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

@@ -53,28 +53,41 @@ instance (p : ℕ) [h : CharP R p] : CharP R[X] p :=
 
 variable (R)
 
+#print Polynomial.degreeLe /-
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree ≤ `n`. -/
 def degreeLe (n : WithBot ℕ) : Submodule R R[X] :=
   ⨅ k : ℕ, ⨅ h : ↑k > n, (lcoeff R k).ker
 #align polynomial.degree_le Polynomial.degreeLe
+-/
 
+#print Polynomial.degreeLt /-
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree < `n`. -/
 def degreeLt (n : ℕ) : Submodule R R[X] :=
   ⨅ k : ℕ, ⨅ h : k ≥ n, (lcoeff R k).ker
 #align polynomial.degree_lt Polynomial.degreeLt
+-/
 
 variable {R}
 
+#print Polynomial.mem_degreeLe /-
 theorem mem_degreeLe {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLe R n ↔ degree f ≤ n := by
   simp only [degree_le, Submodule.mem_infᵢ, degree_le_iff_coeff_zero, LinearMap.mem_ker] <;> rfl
 #align polynomial.mem_degree_le Polynomial.mem_degreeLe
+-/
 
+/- warning: polynomial.degree_le_mono -> Polynomial.degreeLe_mono is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLe.{u1} R _inst_1 m) (Polynomial.degreeLe.{u1} R _inst_1 n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : WithBot.{0} Nat} {n : WithBot.{0} Nat}, (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLe.{u1} R _inst_1 m) (Polynomial.degreeLe.{u1} R _inst_1 n))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_le_mono Polynomial.degreeLe_monoₓ'. -/
 @[mono]
 theorem degreeLe_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLe R m ≤ degreeLe R n := fun f hf =>
   mem_degreeLe.2 (le_trans (mem_degreeLe.1 hf) H)
 #align polynomial.degree_le_mono Polynomial.degreeLe_mono
 
-theorem degreeLe_eq_span_x_pow {n : ℕ} :
+#print Polynomial.degreeLe_eq_span_X_pow /-
+theorem degreeLe_eq_span_X_pow {n : ℕ} :
     degreeLe R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) :=
   by
   apply le_antisymm
@@ -94,8 +107,10 @@ theorem degreeLe_eq_span_x_pow {n : ℕ} :
   intro k hk; apply mem_degree_le.2
   exact
     (degree_X_pow_le _).trans (WithBot.coe_le_coe.2 <| Nat.le_of_lt_succ <| Finset.mem_range.1 hk)
-#align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLe_eq_span_x_pow
+#align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLe_eq_span_X_pow
+-/
 
+#print Polynomial.mem_degreeLt /-
 theorem mem_degreeLt {n : ℕ} {f : R[X]} : f ∈ degreeLt R n ↔ degree f < n :=
   by
   simp_rw [degree_lt, Submodule.mem_infᵢ, LinearMap.mem_ker, degree, Finset.max_eq_sup_coe,
@@ -103,13 +118,21 @@ theorem mem_degreeLt {n : ℕ} {f : R[X]} : f ∈ degreeLt R n ↔ degree f < n
     Ne, not_imp_not]
   rfl
 #align polynomial.mem_degree_lt Polynomial.mem_degreeLt
+-/
 
+/- warning: polynomial.degree_lt_mono -> Polynomial.degreeLt_mono is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.partialOrder.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))))) (Polynomial.degreeLt.{u1} R _inst_1 m) (Polynomial.degreeLt.{u1} R _inst_1 n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Preorder.toLE.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (PartialOrder.toPreorder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Submodule.completeLattice.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))) (Polynomial.degreeLt.{u1} R _inst_1 m) (Polynomial.degreeLt.{u1} R _inst_1 n))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_mono Polynomial.degreeLt_monoₓ'. -/
 @[mono]
 theorem degreeLt_mono {m n : ℕ} (H : m ≤ n) : degreeLt R m ≤ degreeLt R n := fun f hf =>
   mem_degreeLt.2 (lt_of_lt_of_le (mem_degreeLt.1 hf) <| WithBot.coe_le_coe.2 H)
 #align polynomial.degree_lt_mono Polynomial.degreeLt_mono
 
-theorem degreeLt_eq_span_x_pow {n : ℕ} :
+#print Polynomial.degreeLt_eq_span_X_pow /-
+theorem degreeLt_eq_span_X_pow {n : ℕ} :
     degreeLt R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) :=
   by
   apply le_antisymm
@@ -127,8 +150,10 @@ theorem degreeLt_eq_span_x_pow {n : ℕ} :
   rw [Submodule.span_le, Finset.coe_image, Set.image_subset_iff]
   intro k hk; apply mem_degree_lt.2
   exact lt_of_le_of_lt (degree_X_pow_le _) (WithBot.coe_lt_coe.2 <| Finset.mem_range.1 hk)
-#align polynomial.degree_lt_eq_span_X_pow Polynomial.degreeLt_eq_span_x_pow
+#align polynomial.degree_lt_eq_span_X_pow Polynomial.degreeLt_eq_span_X_pow
+-/
 
+#print Polynomial.degreeLtEquiv /-
 /-- The first `n` coefficients on `degree_lt n` form a linear equivalence with `fin n → R`. -/
 def degreeLtEquiv (R) [Semiring R] (n : ℕ) : degreeLt R n ≃ₗ[R] Fin n → R
     where
@@ -164,13 +189,26 @@ def degreeLtEquiv (R) [Semiring R] (n : ℕ) : degreeLt R n ≃ₗ[R] Fin n →
     · intro h
       exact (h (Finset.mem_univ _)).elim
 #align polynomial.degree_lt_equiv Polynomial.degreeLtEquiv
+-/
 
+/- warning: polynomial.degree_lt_equiv_eq_zero_iff_eq_zero -> Polynomial.degreeLtEquiv_eq_zero_iff_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} {p : Polynomial.{u1} R _inst_1} (hp : Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R 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(RingHomInvPair.ids.{u1} R _inst_1)) (Polynomial.degreeLtEquiv.{u1} R _inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.Mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n)) p hp)) (OfNat.ofNat.{u1} ((Fin n) -> R) 0 (OfNat.mk.{u1} ((Fin n) -> R) 0 (Zero.zero.{u1} ((Fin n) -> R) (Pi.instZero.{0, u1} (Fin n) (fun (ᾰ : Fin n) => R) (fun (i : Fin n) => MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))))) (Eq.{succ u1} (Polynomial.{u1} R _inst_1) p (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
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(Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) p (Polynomial.degreeLt.{u1} R _inst_1 n)), Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) => (Fin n) -> R) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R 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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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (fun (_x : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) => (Fin n) -> R) _x) (SMulHomClass.toFunLike.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (SMulZeroClass.toSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddMonoid.toZero.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddMonoid.toAddZeroClass.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} 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R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1))) R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLtEquiv_eq_zero_iff_eq_zeroₓ'. -/
 @[simp]
 theorem degreeLtEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n) :
     degreeLtEquiv _ _ ⟨p, hp⟩ = 0 ↔ p = 0 := by
   rw [LinearEquiv.map_eq_zero_iff, Submodule.mk_eq_zero]
 #align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLtEquiv_eq_zero_iff_eq_zero
 
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+but is expected to have type
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_inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R 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R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))) (DistribMulAction.toDistribSMul.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n))) (Module.toDistribMulAction.{u1, u1} R (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) _inst_1 (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Submodule.module.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)))))) (SMulZeroClass.toSMul.{u1, u1} R ((Fin n) -> R) (AddMonoid.toZero.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribSMul.toSMulZeroClass.{u1, u1} R ((Fin n) -> R) (AddMonoid.toAddZeroClass.{u1} ((Fin n) -> R) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (DistribMulAction.toDistribSMul.{u1, u1} R ((Fin n) -> R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} ((Fin n) -> R) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u1} R ((Fin n) -> R) _inst_1 (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Pi.module.{0, u1, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) R _inst_1 (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (fun (i : Fin n) => Semiring.toModule.{u1} R _inst_1)))))) (DistribMulActionHomClass.toSMulHomClass.{u1, u1, u1, u1} (LinearEquiv.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)))) x (Polynomial.degreeLt.{u1} R _inst_1 n))) ((Fin n) -> R) (Submodule.addCommMonoid.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.degreeLt.{u1} R _inst_1 n)) (Pi.addCommMonoid.{0, u1} (Fin n) (fun (a._@.Mathlib.RingTheory.Polynomial.Basic._hyg.1130 : Fin n) => R) (fun (i : Fin n) => NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Submodule.module.{u1, 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_inst_1 n) (Subtype.mk.{succ u1} (Polynomial.{u1} R _inst_1) (fun (x : Polynomial.{u1} R _inst_1) => Membership.mem.{u1, u1} (Polynomial.{u1} R _inst_1) (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R _inst_1) _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)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) 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+Case conversion may be inaccurate. Consider using '#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLtEquivₓ'. -/
 theorem eval_eq_sum_degreeLtEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n) (x : R) :
     p.eval x = ∑ i, degreeLtEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
   by
@@ -178,19 +216,30 @@ theorem eval_eq_sum_degreeLtEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n)
   exact (sum_fin _ (by simp_rw [MulZeroClass.zero_mul, forall_const]) (mem_degree_lt.mp hp)).symm
 #align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLtEquiv
 
+#print Polynomial.frange /-
 /-- The finset of nonzero coefficients of a polynomial. -/
 def frange (p : R[X]) : Finset R :=
   Finset.image (fun n => p.coeff n) p.support
 #align polynomial.frange Polynomial.frange
+-/
 
+#print Polynomial.frange_zero /-
 theorem frange_zero : frange (0 : R[X]) = ∅ :=
   rfl
 #align polynomial.frange_zero Polynomial.frange_zero
+-/
 
+/- warning: polynomial.mem_frange_iff -> Polynomial.mem_frange_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {c : R}, Iff (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) c (Polynomial.frange.{u1} R _inst_1 p)) (Exists.{1} Nat (fun (n : Nat) => Exists.{0} (Membership.Mem.{0, 0} Nat (Finset.{0} Nat) (Finset.hasMem.{0} Nat) n (Polynomial.support.{u1} R _inst_1 p)) (fun (H : Membership.Mem.{0, 0} Nat (Finset.{0} Nat) (Finset.hasMem.{0} Nat) n (Polynomial.support.{u1} R _inst_1 p)) => Eq.{succ u1} R c (Polynomial.coeff.{u1} R _inst_1 p n))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {p : Polynomial.{u1} R _inst_1} {c : R}, Iff (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) c (Polynomial.frange.{u1} R _inst_1 p)) (Exists.{1} Nat (fun (n : Nat) => And (Membership.mem.{0, 0} Nat (Finset.{0} Nat) (Finset.instMembershipFinset.{0} Nat) n (Polynomial.support.{u1} R _inst_1 p)) (Eq.{succ u1} R c (Polynomial.coeff.{u1} R _inst_1 p n))))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_frange_iff Polynomial.mem_frange_iffₓ'. -/
 theorem mem_frange_iff {p : R[X]} {c : R} : c ∈ p.frange ↔ ∃ n ∈ p.support, c = p.coeff n := by
   simp [frange, eq_comm]
 #align polynomial.mem_frange_iff Polynomial.mem_frange_iff
 
+#print Polynomial.frange_one /-
 theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
   by
   simp [frange, Finset.image_subset_iff]
@@ -199,14 +248,22 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} :=
   simp only [exists_prop, ite_eq_right_iff, not_forall] at hn
   simp [hn]
 #align polynomial.frange_one Polynomial.frange_one
+-/
 
+/- warning: polynomial.coeff_mem_frange -> Polynomial.coeff_mem_frange is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (Ne.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 p n) (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)))))))) -> (Membership.Mem.{u1, u1} R (Finset.{u1} R) (Finset.hasMem.{u1} R) (Polynomial.coeff.{u1} R _inst_1 p n) (Polynomial.frange.{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) (n : Nat), (Ne.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 p n) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Membership.mem.{u1, u1} R (Finset.{u1} R) (Finset.instMembershipFinset.{u1} R) (Polynomial.coeff.{u1} R _inst_1 p n) (Polynomial.frange.{u1} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_mem_frange Polynomial.coeff_mem_frangeₓ'. -/
 theorem coeff_mem_frange (p : R[X]) (n : ℕ) (h : p.coeff n ≠ 0) : p.coeff n ∈ p.frange :=
   by
   simp only [frange, exists_prop, mem_support_iff, Finset.mem_image, Ne.def]
   exact ⟨n, h, rfl⟩
 #align polynomial.coeff_mem_frange Polynomial.coeff_mem_frange
 
-theorem geom_sum_x_comp_x_add_one_eq_sum (n : ℕ) :
+#print Polynomial.geom_sum_X_comp_X_add_one_eq_sum /-
+theorem geom_sum_X_comp_X_add_one_eq_sum (n : ℕ) :
     (∑ i in range n, (X : R[X]) ^ i).comp (X + 1) =
       (Finset.range n).Sum fun i : ℕ => (n.choose (i + 1) : R[X]) * X ^ i :=
   by
@@ -224,8 +281,10 @@ theorem geom_sum_x_comp_x_add_one_eq_sum (n : ℕ) :
   · simp only [geom_sum_zero, zero_comp, coeff_zero, Nat.choose_zero_succ, Nat.cast_zero]
   simp only [geom_sum_succ', ih, add_comp, X_pow_comp, coeff_add, Nat.choose_succ_succ,
     Nat.cast_add, coeff_X_add_one_pow]
-#align polynomial.geom_sum_X_comp_X_add_one_eq_sum Polynomial.geom_sum_x_comp_x_add_one_eq_sum
+#align polynomial.geom_sum_X_comp_X_add_one_eq_sum Polynomial.geom_sum_X_comp_X_add_one_eq_sum
+-/
 
+#print Polynomial.Monic.geom_sum /-
 theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : ℕ} (hn : n ≠ 0) :
     (∑ i in range n, P ^ i).Monic := by
   nontriviality R
@@ -241,18 +300,23 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
   · rw [bot_lt_iff_ne_bot, Ne.def, degree_eq_bot]
     exact (hP.pow _).NeZero
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
+-/
 
+#print Polynomial.Monic.geom_sum' /-
 theorem Monic.geom_sum' {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.degree) {n : ℕ} (hn : n ≠ 0) :
     (∑ i in range n, P ^ i).Monic :=
   hP.geom_sum (natDegree_pos_iff_degree_pos.2 hdeg) hn
 #align polynomial.monic.geom_sum' Polynomial.Monic.geom_sum'
+-/
 
-theorem monic_geom_sum_x {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (X : R[X]) ^ i).Monic :=
+#print Polynomial.monic_geom_sum_X /-
+theorem monic_geom_sum_X {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (X : R[X]) ^ i).Monic :=
   by
   nontriviality R
   apply monic_X.geom_sum _ hn
   simpa only [nat_degree_X] using zero_lt_one
-#align polynomial.monic_geom_sum_X Polynomial.monic_geom_sum_x
+#align polynomial.monic_geom_sum_X Polynomial.monic_geom_sum_X
+-/
 
 end Semiring
 
@@ -260,6 +324,12 @@ section Ring
 
 variable [Ring R]
 
+/- warning: polynomial.restriction -> Polynomial.restriction is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.restriction Polynomial.restrictionₓ'. -/
 /-- Given a polynomial, return the polynomial whose coefficients are in
 the ring closure of the original coefficients. -/
 def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R)) :=
@@ -271,6 +341,7 @@ def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R))
         Subring.closure (↑p.frange : Set R))
 #align polynomial.restriction Polynomial.restriction
 
+#print Polynomial.coeff_restriction /-
 @[simp]
 theorem coeff_restriction {p : R[X]} {n : ℕ} : ↑(coeff (restriction p) n) = coeff p n :=
   by
@@ -281,12 +352,16 @@ theorem coeff_restriction {p : R[X]} {n : ℕ} : ↑(coeff (restriction p) n) =
     rfl
   · rfl
 #align polynomial.coeff_restriction Polynomial.coeff_restriction
+-/
 
+#print Polynomial.coeff_restriction' /-
 @[simp]
 theorem coeff_restriction' {p : R[X]} {n : ℕ} : (coeff (restriction p) n).1 = coeff p n :=
   coeff_restriction
 #align polynomial.coeff_restriction' Polynomial.coeff_restriction'
+-/
 
+#print Polynomial.support_restriction /-
 @[simp]
 theorem support_restriction (p : R[X]) : support (restriction p) = support p :=
   by
@@ -298,22 +373,39 @@ theorem support_restriction (p : R[X]) : support (restriction p) = support p :=
       rw [H]
       rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.support_restriction Polynomial.support_restriction
+-/
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_restriction Polynomial.map_restrictionₓ'. -/
 @[simp]
 theorem map_restriction {R : Type u} [CommRing R] (p : R[X]) :
     p.restriction.map (algebraMap _ _) = p :=
   ext fun n => by rw [coeff_map, Algebra.algebraMap_ofSubring_apply, coeff_restriction]
 #align polynomial.map_restriction Polynomial.map_restriction
 
+#print Polynomial.degree_restriction /-
 @[simp]
 theorem degree_restriction {p : R[X]} : (restriction p).degree = p.degree := by simp [degree]
 #align polynomial.degree_restriction Polynomial.degree_restriction
+-/
 
+#print Polynomial.natDegree_restriction /-
 @[simp]
 theorem natDegree_restriction {p : R[X]} : (restriction p).natDegree = p.natDegree := by
   simp [nat_degree]
 #align polynomial.nat_degree_restriction Polynomial.natDegree_restriction
+-/
 
+/- warning: polynomial.monic_restriction -> Polynomial.monic_restriction is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.monic_restriction Polynomial.monic_restrictionₓ'. -/
 @[simp]
 theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
   by
@@ -325,11 +417,23 @@ theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p :=
       rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_restriction Polynomial.monic_restriction
 
+/- warning: polynomial.restriction_zero -> Polynomial.restriction_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.restriction_zero Polynomial.restriction_zeroₓ'. -/
 @[simp]
 theorem restriction_zero : restriction (0 : R[X]) = 0 := by
   simp only [restriction, Finset.sum_empty, support_zero]
 #align polynomial.restriction_zero Polynomial.restriction_zero
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.restriction_one Polynomial.restriction_oneₓ'. -/
 @[simp]
 theorem restriction_one : restriction (1 : R[X]) = 1 :=
   ext fun i => Subtype.eq <| by rw [coeff_restriction', coeff_one, coeff_one] <;> split_ifs <;> rfl
@@ -337,6 +441,12 @@ theorem restriction_one : restriction (1 : R[X]) = 1 :=
 
 variable [Semiring S] {f : R →+* S} {x : S}
 
+/- warning: polynomial.eval₂_restriction -> Polynomial.eval₂_restriction is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.eval₂_restriction Polynomial.eval₂_restrictionₓ'. -/
 theorem eval₂_restriction {p : R[X]} :
     eval₂ f x p =
       eval₂ (f.comp (Subring.subtype (Subring.closure (p.frange : Set R)))) x p.restriction :=
@@ -349,6 +459,12 @@ section ToSubring
 
 variable (p : R[X]) (T : Subring R)
 
+/- warning: polynomial.to_subring -> Polynomial.toSubring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_subring Polynomial.toSubringₓ'. -/
 /-- Given a polynomial `p` and a subring `T` that contains the coefficients of `p`,
 return the corresponding polynomial whose coefficients are in `T`. -/
 def toSubring (hp : (↑p.frange : Set R) ⊆ T) : T[X] :=
@@ -362,6 +478,12 @@ variable (hp : (↑p.frange : Set R) ⊆ T)
 
 include hp
 
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 @[simp]
 theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n :=
   by
@@ -373,11 +495,23 @@ theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n
   · rfl
 #align polynomial.coeff_to_subring Polynomial.coeff_toSubring
 
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 @[simp]
 theorem coeff_to_subring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
   coeff_toSubring _ _ hp
 #align polynomial.coeff_to_subring' Polynomial.coeff_to_subring'
 
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 @[simp]
 theorem support_toSubring : support (toSubring p T hp) = support p :=
   by
@@ -390,14 +524,32 @@ theorem support_toSubring : support (toSubring p T hp) = support p :=
       rfl, fun H => Subtype.coe_injective H⟩
 #align polynomial.support_to_subring Polynomial.support_toSubring
 
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 @[simp]
 theorem degree_toSubring : (toSubring p T hp).degree = p.degree := by simp [degree]
 #align polynomial.degree_to_subring Polynomial.degree_toSubring
 
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 @[simp]
 theorem natDegree_toSubring : (toSubring p T hp).natDegree = p.natDegree := by simp [nat_degree]
 #align polynomial.nat_degree_to_subring Polynomial.natDegree_toSubring
 
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 @[simp]
 theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
   by
@@ -410,6 +562,12 @@ theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p :=
 
 omit hp
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_subring_zero Polynomial.toSubring_zeroₓ'. -/
 @[simp]
 theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 :=
   by
@@ -417,6 +575,12 @@ theorem toSubring_zero : toSubring (0 : R[X]) T (by simp [frange_zero]) = 0 :=
   simp
 #align polynomial.to_subring_zero Polynomial.toSubring_zero
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.to_subring_one Polynomial.toSubring_oneₓ'. -/
 @[simp]
 theorem toSubring_one :
     toSubring (1 : R[X]) T
@@ -425,6 +589,12 @@ theorem toSubring_one :
   ext fun i => Subtype.eq <| by rw [coeff_to_subring', coeff_one, coeff_one] <;> split_ifs <;> rfl
 #align polynomial.to_subring_one Polynomial.toSubring_one
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.map_to_subring Polynomial.map_toSubringₓ'. -/
 @[simp]
 theorem map_toSubring : (p.toSubring T hp).map (Subring.subtype T) = p :=
   by
@@ -436,12 +606,24 @@ end ToSubring
 
 variable (T : Subring R)
 
+/- warning: polynomial.of_subring -> Polynomial.ofSubring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.of_subring Polynomial.ofSubringₓ'. -/
 /-- Given a polynomial whose coefficients are in some subring, return
 the corresponding polynomial whose coefficients are in the ambient ring. -/
 def ofSubring (p : T[X]) : R[X] :=
   ∑ i in p.support, monomial i (p.coeff i : R)
 #align polynomial.of_subring Polynomial.ofSubring
 
+/- warning: polynomial.coeff_of_subring -> Polynomial.coeff_ofSubring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_of_subring Polynomial.coeff_ofSubringₓ'. -/
 theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff p n : T) :=
   by
   simp only [of_subring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
@@ -451,6 +633,12 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
   rfl
 #align polynomial.coeff_of_subring Polynomial.coeff_ofSubring
 
+/- warning: polynomial.frange_of_subring -> Polynomial.frange_ofSubring is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.frange_of_subring Polynomial.frange_ofSubringₓ'. -/
 @[simp]
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T :=
   by
@@ -471,10 +659,22 @@ section ModByMonic
 
 variable {q : R[X]}
 
+/- warning: polynomial.mem_ker_mod_by_monic -> Polynomial.mem_ker_mod_by_monic is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SetLike.hasMem.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) p (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.semilinearMapClass.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q))) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commRing.{u1} R _inst_1))))))) q p))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (SetLike.instMembership.{u1, u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Submodule.setLike.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) p (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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+Case conversion may be inaccurate. Consider using '#align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monicₓ'. -/
 theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} : p ∈ (modByMonicHom q).ker ↔ q ∣ p :=
   LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
 #align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monic
 
+/- warning: polynomial.ker_mod_by_monic_hom -> Polynomial.ker_modByMonicHom is a dubious translation:
+lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toAddCommGroup.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.hasSingleton.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) q))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) q) -> (Eq.{succ u1} (Submodule.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.ker.{u1, u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.modByMonicHom.{u1} R _inst_1 q)) (Submodule.restrictScalars.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_1 (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Algebra.toSMul.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.isScalarTower_right.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (DistribMulAction.toDistribSMul.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRing.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_1 (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (IsScalarTower.right.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Ideal.span.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Set.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Set.instSingletonSet.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) q))))
+Case conversion may be inaccurate. Consider using '#align polynomial.ker_mod_by_monic_hom Polynomial.ker_modByMonicHomₓ'. -/
 @[simp]
 theorem ker_modByMonicHom (hq : q.Monic) :
     (Polynomial.modByMonicHom q).ker = (Ideal.span {q}).restrictScalars R :=
@@ -495,6 +695,7 @@ section Semiring
 
 variable [Semiring R]
 
+#print Ideal.ofPolynomial /-
 /-- Transport an ideal of `R[X]` to an `R`-submodule of `R[X]`. -/
 def ofPolynomial (I : Ideal R[X]) : Submodule R R[X]
     where
@@ -505,32 +706,41 @@ def ofPolynomial (I : Ideal R[X]) : Submodule R R[X]
     rw [← C_mul']
     exact I.mul_mem_left _ H
 #align ideal.of_polynomial Ideal.ofPolynomial
+-/
 
 variable {I : Ideal R[X]}
 
+#print Ideal.mem_ofPolynomial /-
 theorem mem_ofPolynomial (x) : x ∈ I.ofPolynomial ↔ x ∈ I :=
   Iff.rfl
 #align ideal.mem_of_polynomial Ideal.mem_ofPolynomial
+-/
 
 variable (I)
 
+#print Ideal.degreeLe /-
 /-- Given an ideal `I` of `R[X]`, make the `R`-submodule of `I`
 consisting of polynomials of degree ≤ `n`. -/
 def degreeLe (n : WithBot ℕ) : Submodule R R[X] :=
   degreeLe R n ⊓ I.ofPolynomial
 #align ideal.degree_le Ideal.degreeLe
+-/
 
+#print Ideal.leadingCoeffNth /-
 /-- Given an ideal `I` of `R[X]`, make the ideal in `R` of
 leading coefficients of polynomials in `I` with degree ≤ `n`. -/
 def leadingCoeffNth (n : ℕ) : Ideal R :=
   (I.degreeLe n).map <| lcoeff R n
 #align ideal.leading_coeff_nth Ideal.leadingCoeffNth
+-/
 
+#print Ideal.leadingCoeff /-
 /-- Given an ideal `I` in `R[X]`, make the ideal in `R` of the
 leading coefficients in `I`. -/
 def leadingCoeff : Ideal R :=
   ⨆ n : ℕ, I.leadingCoeffNth n
 #align ideal.leading_coeff Ideal.leadingCoeff
+-/
 
 end Semiring
 
@@ -538,15 +748,27 @@ section CommSemiring
 
 variable [CommSemiring R] [Semiring S]
 
+/- warning: ideal.polynomial_mem_ideal_of_coeff_mem_ideal -> Ideal.polynomial_mem_ideal_of_coeff_mem_ideal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (forall (n : Nat), Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p n) (Ideal.comap.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) I)) -> (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), (forall (n : Nat), Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p n) (Ideal.comap.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) I)) -> (Membership.mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I)
+Case conversion may be inaccurate. Consider using '#align ideal.polynomial_mem_ideal_of_coeff_mem_ideal Ideal.polynomial_mem_ideal_of_coeff_mem_idealₓ'. -/
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself -/
 theorem polynomial_mem_ideal_of_coeff_mem_ideal (I : Ideal R[X]) (p : R[X])
     (hp : ∀ n : ℕ, p.coeff n ∈ I.comap (C : R →+* R[X])) : p ∈ I :=
   sum_C_mul_X_pow_eq p ▸ Submodule.sum_mem I fun n hn => I.mul_mem_right _ (hp n)
 #align ideal.polynomial_mem_ideal_of_coeff_mem_ideal Ideal.polynomial_mem_ideal_of_coeff_mem_ideal
 
+/- warning: ideal.mem_map_C_iff -> Ideal.mem_map_C_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) I)) (forall (n : Nat), Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f n) I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Membership.mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) f (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) I)) (forall (n : Nat), Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f n) I)
+Case conversion may be inaccurate. Consider using '#align ideal.mem_map_C_iff Ideal.mem_map_C_iffₓ'. -/
 /-- The push-forward of an ideal `I` of `R` to `R[X]` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
-theorem mem_map_c_iff {I : Ideal R} {f : R[X]} :
+theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
     f ∈ (Ideal.map (C : R →+* R[X]) I : Ideal R[X]) ↔ ∀ n : ℕ, f.coeff n ∈ I :=
   by
   constructor
@@ -569,8 +791,14 @@ theorem mem_map_c_iff {I : Ideal R} {f : R[X]} :
     simp [← C_mul_X_pow_eq_monomial]
     rw [mul_comm]
     exact (I.map C : Ideal R[X]).mul_mem_left _ (mem_map_of_mem _ (hf n))
-#align ideal.mem_map_C_iff Ideal.mem_map_c_iff
-
+#align ideal.mem_map_C_iff Ideal.mem_map_C_iff
+
+/- warning: polynomial.ker_map_ring_hom -> Polynomial.ker_mapRingHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] (f : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)), Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.ker.{u1, u2, max u1 u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} S _inst_2) (RingHom.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u2} S _inst_2) (RingHom.ringHomClass.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))) (Polynomial.mapRingHom.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 f)) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHom.ker.{u1, u2, max u1 u2} R S (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 (RingHom.ringHomClass.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S _inst_2)) f))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} S _inst_2)), Eq.{succ u2} (Submodule.{u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (LinearMap.ker.{u2, u1, u2, u1, max u2 u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f) (LinearMap.{u2, u1, u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} S _inst_2) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2)))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Semiring.toModule.{u1} (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u1} S _inst_2))) (LinearMap.instSemilinearMapClassLinearMap.{u2, u1, u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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_inst_1) _inst_2 f)) (RingHom.toSemilinearMap.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u1} S _inst_2) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u1} S _inst_2) (Polynomial.mapRingHom.{u2, u1} R S (CommSemiring.toSemiring.{u2} R _inst_1) _inst_2 f))) (Ideal.map.{u2, u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (CommSemiring.toSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (RingHom.instRingHomClassRingHom.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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+Case conversion may be inaccurate. Consider using '#align polynomial.ker_map_ring_hom Polynomial.ker_mapRingHomₓ'. -/
 theorem Polynomial.ker_mapRingHom (f : R →+* S) :
     (Polynomial.mapRingHom f).ker = f.ker.map (C : R →+* R[X]) :=
   by
@@ -581,6 +809,12 @@ theorem Polynomial.ker_mapRingHom (f : R →+* S) :
 
 variable (I : Ideal R[X])
 
+/- warning: ideal.mem_leading_coeff_nth -> Ideal.mem_leadingCoeffNth is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (n : Nat) (x : R), Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n)) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{0} (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) (fun (H : Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) => And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat (WithBot.{0} Nat) (HasLiftT.mk.{1, 1} Nat (WithBot.{0} Nat) (CoeTCₓ.coe.{1, 1} Nat (WithBot.{0} Nat) (WithBot.hasCoeT.{0} Nat))) n)) (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) x))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (n : Nat) (x : R), Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n)) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Membership.mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) (And (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) (Nat.cast.{0} (WithBot.{0} Nat) (Semiring.toNatCast.{0} (WithBot.{0} Nat) (OrderedSemiring.toSemiring.{0} (WithBot.{0} Nat) (OrderedCommSemiring.toOrderedSemiring.{0} (WithBot.{0} Nat) (WithBot.orderedCommSemiring.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) Nat.canonicallyOrderedCommSemiring Nat.nontrivial)))) n)) (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) x))))
+Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNthₓ'. -/
 theorem mem_leadingCoeffNth (n : ℕ) (x) :
     x ∈ I.leadingCoeffNth n ↔ ∃ p ∈ I, degree p ≤ n ∧ p.leadingCoeff = x :=
   by
@@ -606,6 +840,12 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
     · rw [Polynomial.leadingCoeff, ← coeff_mul_X_pow p (n - nat_degree p), this]
 #align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNth
 
+/- warning: ideal.mem_leading_coeff_nth_zero -> Ideal.mem_leadingCoeffNth_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) => R -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) I)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{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)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{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))))))) (Polynomial.C.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) x) I)
+Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zeroₓ'. -/
 theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :=
   (mem_leadingCoeffNth _ _ _).trans
     ⟨fun ⟨p, hpI, hpdeg, hpx⟩ => by
@@ -614,6 +854,12 @@ theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :
       fun hx => ⟨C x, hx, degree_C_le, leadingCoeff_C x⟩⟩
 #align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zero
 
+/- warning: ideal.leading_coeff_nth_mono -> Ideal.leadingCoeffNth_mono is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.partialOrder.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I m) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Preorder.toLE.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (PartialOrder.toPreorder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.completeLattice.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I m) (Ideal.leadingCoeffNth.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I n))
+Case conversion may be inaccurate. Consider using '#align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_monoₓ'. -/
 theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤ I.leadingCoeffNth n :=
   by
   intro r hr
@@ -626,6 +872,12 @@ theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤
   exact le_rfl
 #align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_mono
 
+/- warning: ideal.mem_leading_coeff -> Ideal.mem_leadingCoeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Iff (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I)) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => Exists.{0} (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) (fun (H : Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) => Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) x)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] (I : Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (x : R), Iff (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) x (Ideal.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) I)) (Exists.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => And (Membership.mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{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))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p I) (Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) p) x)))
+Case conversion may be inaccurate. Consider using '#align ideal.mem_leading_coeff Ideal.mem_leadingCoeffₓ'. -/
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x :=
   by
   rw [leading_coeff, Submodule.mem_supᵢ_of_directed]
@@ -641,6 +893,12 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
       I.leading_coeff_nth_mono (Nat.le_add_left _ _)⟩
 #align ideal.mem_leading_coeff Ideal.mem_leadingCoeff
 
+/- warning: polynomial.coeff_prod_mem_ideal_pow_tsub -> Polynomial.coeff_prod_mem_ideal_pow_tsub is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (n : ι -> Nat), (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (forall (k : Nat), Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (f i) k) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.idemSemiring.{u1, u1} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (n i) k)))) -> (forall (k : Nat), Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) (Finset.prod.{u1, u2} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ι (CommSemiring.toCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.commSemiring.{u1} R _inst_1)) s f) k) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.idemSemiring.{u1, u1} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Finset.sum.{0, u2} Nat ι Nat.addCommMonoid s n) k)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (I : Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (n : ι -> Nat), (forall (i : ι), (Membership.mem.{u1, u1} ι (Finset.{u1} ι) (Finset.instMembershipFinset.{u1} ι) i s) -> (forall (k : Nat), Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.coeff.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) (f i) k) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.idemSemiring.{u2, u2} R _inst_1 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (n i) k)))) -> (forall (k : Nat), Membership.mem.{u2, u2} R (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (SetLike.instMembership.{u2, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) R (Submodule.setLike.{u2, u2} R R (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (Polynomial.coeff.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1) (Finset.prod.{u2, u1} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) ι (CommSemiring.toCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.commSemiring.{u2} R _inst_1)) s f) k) (HPow.hPow.{u2, 0, u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) Nat (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (instHPow.{u2, 0} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) Nat (Monoid.Pow.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toMonoidWithZero.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (IdemSemiring.toSemiring.{u2} (Ideal.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.idemSemiring.{u2, u2} R _inst_1 R (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) I (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Finset.sum.{0, u1} Nat ι Nat.addCommMonoid s n) k)))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_prod_mem_ideal_pow_tsub Polynomial.coeff_prod_mem_ideal_pow_tsubₓ'. -/
 /-- If `I` is an ideal, and `pᵢ` is a finite family of polynomials each satisfying
 `∀ k, (pᵢ)ₖ ∈ Iⁿⁱ⁻ᵏ` for some `nᵢ`, then `p = ∏ pᵢ` also satisfies `∀ k, pₖ ∈ Iⁿ⁻ᵏ` with `n = ∑ nᵢ`.
 -/
@@ -668,6 +926,7 @@ section Ring
 
 variable [Ring R]
 
+#print Ideal.polynomial_not_isField /-
 /-- `R[X]` is never a field for any ring `R`. -/
 theorem polynomial_not_isField : ¬IsField R[X] :=
   by
@@ -682,7 +941,14 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
   rw [← X_mul, congr_arg degree hp, degree_one, Nat.WithBot.lt_zero_iff, degree_eq_bot] at this
   exact hp0 this
 #align ideal.polynomial_not_is_field Ideal.polynomial_not_isField
+-/
 
+/- warning: ideal.eq_zero_of_constant_mem_of_maximal -> Ideal.eq_zero_of_constant_mem_of_maximal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (IsField.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (forall (I : Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) [hI : Ideal.IsMaximal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I] (x : R), (Membership.Mem.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) I) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R _inst_1))))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Ring.{u1} R], (IsField.{u1} R (Ring.toSemiring.{u1} R _inst_1)) -> (forall (I : Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) [hI : Ideal.IsMaximal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) I] (x : R), (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_1))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_1)) x) I) -> (Eq.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R _inst_1)))))))
+Case conversion may be inaccurate. Consider using '#align ideal.eq_zero_of_constant_mem_of_maximal Ideal.eq_zero_of_constant_mem_of_maximalₓ'. -/
 /-- The only constant in a maximal ideal over a field is `0`. -/
 theorem eq_zero_of_constant_mem_of_maximal (hR : IsField R) (I : Ideal R[X]) [hI : I.IsMaximal]
     (x : R) (hx : C x ∈ I) : x = 0 :=
@@ -699,8 +965,14 @@ section CommRing
 
 variable [CommRing R]
 
+/- warning: ideal.is_prime_map_C_iff_is_prime -> Ideal.isPrime_map_C_iff_isPrime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Iff (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P)) (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] (P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))), Iff (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P)) (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P)
+Case conversion may be inaccurate. Consider using '#align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrimeₓ'. -/
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
-theorem isPrime_map_c_iff_isPrime (P : Ideal R) :
+theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) ↔ IsPrime P :=
   by
   -- Porting note: the following proof avoids quotient rings
@@ -756,19 +1028,27 @@ theorem isPrime_map_c_iff_isPrime (P : Ideal R) :
           exact Classical.not_not.1 (Nat.find_min hf hi)
         · apply P.mul_mem_left
           exact Classical.not_not.1 (Nat.find_min hg hj)
-#align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_c_iff_isPrime
-
+#align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_C_iff_isPrime
+
+/- warning: ideal.is_prime_map_C_of_is_prime -> Ideal.isPrime_map_C_of_isPrime is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P) -> (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {P : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) P) -> (Ideal.IsPrime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ideal.map.{u1, u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) P))
+Case conversion may be inaccurate. Consider using '#align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrimeₓ'. -/
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
-theorem isPrime_map_c_of_isPrime {P : Ideal R} (H : IsPrime P) :
+theorem isPrime_map_C_of_isPrime {P : Ideal R} (H : IsPrime P) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) :=
-  (isPrime_map_c_iff_isPrime P).mpr H
-#align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_c_of_isPrime
+  (isPrime_map_C_iff_isPrime P).mpr H
+#align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrime
 
+#print Ideal.is_fg_degreeLe /-
 theorem is_fg_degreeLe [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
     Submodule.Fg (I.degreeLe n) :=
   isNoetherian_submodule_left.1
-    (isNoetherian_of_fg_of_noetherian _ ⟨_, degreeLe_eq_span_x_pow.symm⟩) _
+    (isNoetherian_of_fg_of_noetherian _ ⟨_, degreeLe_eq_span_X_pow.symm⟩) _
 #align ideal.is_fg_degree_le Ideal.is_fg_degreeLe
+-/
 
 end CommRing
 
@@ -784,15 +1064,21 @@ variable (σ) {r : R}
 
 namespace Polynomial
 
-theorem prime_c_iff : Prime (C r) ↔ Prime r :=
+/- warning: polynomial.prime_C_iff -> Polynomial.prime_C_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (CommSemiring.toCommMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r) (Polynomial.commRing.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
+Case conversion may be inaccurate. Consider using '#align polynomial.prime_C_iff Polynomial.prime_C_iffₓ'. -/
+theorem prime_C_iff : Prime (C r) ↔ Prime r :=
   ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr =>
     by
     have := hr.1
     rw [← Ideal.span_singleton_prime] at hr⊢
-    · convert Ideal.isPrime_map_c_of_isPrime hr using 1
+    · convert Ideal.isPrime_map_C_of_isPrime hr using 1
       rw [Ideal.map_span, Set.image_singleton]
     exacts[fun h => this (C_eq_zero.1 h), this]⟩
-#align polynomial.prime_C_iff Polynomial.prime_c_iff
+#align polynomial.prime_C_iff Polynomial.prime_C_iff
 
 end Polynomial
 
@@ -807,13 +1093,19 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial
   · symm
     induction' Fintype.card σ with d hd
     · exact (is_empty_alg_equiv R (Fin 0)).toMulEquiv.symm.prime_iff
-    · rw [hd, ← Polynomial.prime_c_iff]
+    · rw [hd, ← Polynomial.prime_C_iff]
       convert(finSuccEquiv R d).toMulEquiv.symm.prime_iff
       rw [← fin_succ_equiv_comp_C_eq_C]
       rfl
 #align mv_polynomial.prime_C_iff_of_fintype mv_polynomial.prime_C_iff_of_fintype
 
-theorem prime_c_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
+/- warning: mv_polynomial.prime_C_iff -> MvPolynomial.prime_C_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (σ : Type.{u2}) [_inst_1 : CommRing.{u1} R] {r : R}, Iff (Prime.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toCommMonoidWithZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ u1) (succ (max u2 u1))} (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) => R -> (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.hasCoeToFun.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
+but is expected to have type
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_inst_1))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, max u2 u1} (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.instRingHomClassRingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) r)) (Prime.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) r)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iffₓ'. -/
+theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   ⟨comap_prime C constantCoeff (constantCoeff_C _), fun hr =>
     ⟨fun h =>
       hr.1 <| by
@@ -834,10 +1126,11 @@ theorem prime_c_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       rw [← rename_C (coe : s → σ)]
       let f := (rename (coe : s → σ)).toRingHom
       exact (((prime_C_iff_of_fintype s).2 hr).2.2 a' b' this).imp f.map_dvd f.map_dvd⟩⟩
-#align mv_polynomial.prime_C_iff MvPolynomial.prime_c_iff
+#align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iff
 
 variable {σ}
 
+#print MvPolynomial.prime_rename_iff /-
 theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     Prime (rename (coe : s → σ) p) ↔ Prime p := by
   classical
@@ -858,6 +1151,7 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
         erw [iter_to_sum_C_X, rename_X, rename_X]
         rfl
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
+-/
 
 end MvPolynomial
 
@@ -898,6 +1192,7 @@ instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R
 
 end Polynomial
 
+#print Polynomial.isNoetherianRing /-
 /-- Hilbert basis theorem: a polynomial ring over a noetherian ring is a noetherian ring. -/
 protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetherianRing R[X] :=
   isNoetherianRing_iff.2
@@ -983,17 +1278,30 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
               rwa [Polynomial.degree_eq_natDegree hpq, WithBot.coe_lt_coe, hn] at this
             exact hs2 ⟨Polynomial.mem_degreeLe.2 hdq, hq⟩⟩⟩
 #align polynomial.is_noetherian_ring Polynomial.isNoetherianRing
+-/
 
 attribute [instance] Polynomial.isNoetherianRing
 
 namespace Polynomial
 
+/- warning: polynomial.exists_irreducible_of_degree_pos -> Polynomial.exists_irreducible_of_degree_pos is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (OfNat.mk.{0} (WithBot.{0} Nat) 0 (Zero.zero.{0} (WithBot.{0} Nat) (WithBot.hasZero.{0} Nat Nat.hasZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} (WithBot.{0} Nat) (Preorder.toLT.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))) (Polynomial.degree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_degree_pos Polynomial.exists_irreducible_of_degree_posₓ'. -/
 theorem exists_irreducible_of_degree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.degree) : ∃ g, Irreducible g ∧ g ∣ f :=
   WfDvdMonoid.exists_irreducible_factor (fun huf => ne_of_gt hf <| degree_eq_zero_of_isUnit huf)
     fun hf0 => not_lt_of_lt hf <| hf0.symm ▸ (@degree_zero R _).symm ▸ WithBot.bot_lt_coe _
 #align polynomial.exists_irreducible_of_degree_pos Polynomial.exists_irreducible_of_degree_pos
 
+/- warning: polynomial.exists_irreducible_of_nat_degree_pos -> Polynomial.exists_irreducible_of_natDegree_pos is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f)) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_nat_degree_pos Polynomial.exists_irreducible_of_natDegree_posₓ'. -/
 theorem exists_irreducible_of_natDegree_pos {R : Type u} [CommRing R] [IsDomain R] [WfDvdMonoid R]
     {f : R[X]} (hf : 0 < f.natDegree) : ∃ g, Irreducible g ∧ g ∣ f :=
   exists_irreducible_of_degree_pos <| by
@@ -1001,11 +1309,23 @@ theorem exists_irreducible_of_natDegree_pos {R : Type u} [CommRing R] [IsDomain
     exact nat_degree_le_of_degree_le hf
 #align polynomial.exists_irreducible_of_nat_degree_pos Polynomial.exists_irreducible_of_natDegree_pos
 
+/- warning: polynomial.exists_irreducible_of_nat_degree_ne_zero -> Polynomial.exists_irreducible_of_natDegree_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_5))) g) (Dvd.Dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
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+  forall {R : Type.{u1}} [_inst_5 : CommRing.{u1} R] [_inst_6 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))] [_inst_7 : WfDvdMonoid.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_5) _inst_6))] {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))}, (Ne.{1} Nat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5)) f) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Exists.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (fun (g : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) => And (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))))) g) (Dvd.dvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (semigroupDvd.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_5))) (Polynomial.commRing.{u1} R _inst_5))))))) g f)))
+Case conversion may be inaccurate. Consider using '#align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zeroₓ'. -/
 theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDomain R]
     [WfDvdMonoid R] {f : R[X]} (hf : f.natDegree ≠ 0) : ∃ g, Irreducible g ∧ g ∣ f :=
   exists_irreducible_of_natDegree_pos <| Nat.pos_of_ne_zero hf
 #align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zero
 
+/- warning: polynomial.linear_independent_powers_iff_aeval -> Polynomial.linearIndependent_powers_iff_aeval is a dubious translation:
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_inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) Nat (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (instHPow.{u2, 0} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M 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+but is expected to have type
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(Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aevalₓ'. -/
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 :=
   by
@@ -1015,6 +1335,7 @@ theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
   exact Iff.rfl
 #align polynomial.linear_independent_powers_iff_aeval Polynomial.linearIndependent_powers_iff_aeval
 
+#print Polynomial.disjoint_ker_aeval_of_coprime /-
 theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     Disjoint (aeval f p).ker (aeval f q).ker :=
   by
@@ -1025,7 +1346,14 @@ theorem disjoint_ker_aeval_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : Is
     LinearMap.mem_ker.1 (Submodule.mem_inf.1 hv).2] using
     congr_arg (fun p : R[X] => aeval f p v) hpq'.symm
 #align polynomial.disjoint_ker_aeval_of_coprime Polynomial.disjoint_ker_aeval_of_coprime
+-/
 
+/- warning: polynomial.sup_aeval_range_eq_top_of_coprime -> Polynomial.sup_aeval_range_eq_top_of_coprime is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprimeₓ'. -/
 theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq : IsCoprime p q) :
     (aeval f p).range ⊔ (aeval f q).range = ⊤ :=
   by
@@ -1041,6 +1369,12 @@ theorem sup_aeval_range_eq_top_of_coprime (f : M →ₗ[R] M) {p q : R[X]} (hpq
     congr_arg (fun p : R[X] => aeval f p v) hpq'
 #align polynomial.sup_aeval_range_eq_top_of_coprime Polynomial.sup_aeval_range_eq_top_of_coprime
 
+/- warning: polynomial.sup_ker_aeval_le_ker_aeval_mul -> Polynomial.sup_ker_aeval_le_ker_aeval_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R 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_inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R 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_inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, 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(CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M 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+Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mulₓ'. -/
 theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
     (aeval f p).ker ⊔ (aeval f q).ker ≤ (aeval f (p * q)).ker :=
   by
@@ -1053,6 +1387,12 @@ theorem sup_ker_aeval_le_ker_aeval_mul {f : M →ₗ[R] M} {p q : R[X]} :
   rw [LinearMap.mem_ker, ← hxy, LinearMap.map_add, h_eval_x, h_eval_y, add_zero]
 #align polynomial.sup_ker_aeval_le_ker_aeval_mul Polynomial.sup_ker_aeval_le_ker_aeval_mul
 
+/- warning: polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime -> Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime is a dubious translation:
+lean 3 declaration is
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(Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) p q))))
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {q : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (IsCoprime.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.commSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) -> (Eq.{succ u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Sup.sup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Submodule.completeLattice.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (LinearMap.ker.{u1, u1, u2, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) => LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) p) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R M M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M 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_inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M 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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) 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_inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R 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(AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Semiring.toNonAssocSemiring.{u2} (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Algebra.toModule.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (AlgHom.algHomClass.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommRing.toCommSemiring.{u1} R _inst_1) (Module.End.semiring.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) (Module.instAlgebraEndToSemiringSemiring.{u1, u2} R M (CommRing.toCommSemiring.{u1} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4) f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) p q))))
+Case conversion may be inaccurate. Consider using '#align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprimeₓ'. -/
 theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X]}
     (hpq : IsCoprime p q) : (aeval f p).ker ⊔ (aeval f q).ker = (aeval f (p * q)).ker :=
   by
@@ -1083,12 +1423,15 @@ end Polynomial
 
 namespace MvPolynomial
 
+#print MvPolynomial.isNoetherianRing_fin_0 /-
 theorem isNoetherianRing_fin_0 [IsNoetherianRing R] : IsNoetherianRing (MvPolynomial (Fin 0) R) :=
   isNoetherianRing_of_ringEquiv R
     ((MvPolynomial.isEmptyRingEquiv R PEmpty).symm.trans
       (renameEquiv R finZeroEquiv'.symm).toRingEquiv)
 #align mv_polynomial.is_noetherian_ring_fin_0 MvPolynomial.isNoetherianRing_fin_0
+-/
 
+#print MvPolynomial.isNoetherianRing_fin /-
 theorem isNoetherianRing_fin [IsNoetherianRing R] :
     ∀ {n : ℕ}, IsNoetherianRing (MvPolynomial (Fin n) R)
   | 0 => isNoetherianRing_fin_0
@@ -1097,7 +1440,9 @@ theorem isNoetherianRing_fin [IsNoetherianRing R] :
       (MvPolynomial.finSuccEquiv _ n).toRingEquiv.symm
       (@Polynomial.isNoetherianRing (MvPolynomial (Fin n) R) _ is_noetherian_ring_fin)
 #align mv_polynomial.is_noetherian_ring_fin MvPolynomial.isNoetherianRing_fin
+-/
 
+#print MvPolynomial.isNoetherianRing /-
 /-- The multivariate polynomial ring in finitely many variables over a noetherian ring
 is itself a noetherian ring. -/
 instance isNoetherianRing [Finite σ] [IsNoetherianRing R] : IsNoetherianRing (MvPolynomial σ R) :=
@@ -1107,7 +1452,14 @@ instance isNoetherianRing [Finite σ] [IsNoetherianRing R] : IsNoetherianRing (M
       @isNoetherianRing_of_ringEquiv (MvPolynomial (Fin (Fintype.card σ)) R) _ _ _
         (rename_equiv R (Fintype.equivFin σ).symm).toRingEquiv is_noetherian_ring_fin
 #align mv_polynomial.is_noetherian_ring MvPolynomial.isNoetherianRing
+-/
 
+/- warning: mv_polynomial.no_zero_divisors_fin -> MvPolynomial.noZeroDivisors_fin is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_5 : CommSemiring.{u1} R] [_inst_6 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))))] (n : Nat), NoZeroDivisors.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (Distrib.toHasMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (NonUnitalNonAssocSemiring.toDistrib.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_5)))))) (MulZeroClass.toHasZero.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_5))))))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_5 : CommSemiring.{u1} R] [_inst_6 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_5))] (n : Nat), NoZeroDivisors.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (NonUnitalNonAssocSemiring.toMul.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (Semiring.toNonAssocSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (CommSemiring.toSemiring.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_5))))) (CommMonoidWithZero.toZero.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (CommSemiring.toCommMonoidWithZero.{u1} (MvPolynomial.{0, u1} (Fin n) R _inst_5) (MvPolynomial.commSemiring.{u1, 0} R (Fin n) _inst_5)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.no_zero_divisors_fin MvPolynomial.noZeroDivisors_finₓ'. -/
 /-- Auxiliary lemma:
 Multivariate polynomials over an integral domain
 with variables indexed by `fin n` form an integral domain.
@@ -1122,6 +1474,12 @@ theorem noZeroDivisors_fin (R : Type u) [CommSemiring R] [NoZeroDivisors R] :
     (MvPolynomial.finSuccEquiv R n).Injective.NoZeroDivisors _ (map_zero _) (map_mul _)
 #align mv_polynomial.no_zero_divisors_fin MvPolynomial.noZeroDivisors_fin
 
+/- warning: mv_polynomial.no_zero_divisors_of_finite -> MvPolynomial.noZeroDivisors_of_finite is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_5 : CommSemiring.{u1} R] [_inst_6 : Finite.{succ u2} σ] [_inst_7 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5))))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))))], NoZeroDivisors.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (Distrib.toHasMul.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (NonUnitalNonAssocSemiring.toDistrib.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_5)))))) (MulZeroClass.toHasZero.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (NonUnitalNonAssocSemiring.toMulZeroClass.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R _inst_5) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_5))))))
+but is expected to have type
+  forall (R : Type.{u1}) (σ : Type.{u2}) [_inst_5 : CommSemiring.{u1} R] [_inst_6 : Finite.{succ u2} σ] [_inst_7 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_5)))) (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_5))], NoZeroDivisors.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_5) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_5) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_5) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_5) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_5) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_5))))) (CommMonoidWithZero.toZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_5) (CommSemiring.toCommMonoidWithZero.{max u1 u2} (MvPolynomial.{u2, u1} σ R _inst_5) (MvPolynomial.commSemiring.{u1, u2} R σ _inst_5)))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.no_zero_divisors_of_finite MvPolynomial.noZeroDivisors_of_finiteₓ'. -/
 /-- Auxiliary definition:
 Multivariate polynomials in finitely many variables over an integral domain form an integral domain.
 This fact is proven by transport of structure from the `mv_polynomial.no_zero_divisors_fin`,
@@ -1162,6 +1520,12 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] : IsDomain (MvPoly
   exact AddMonoidAlgebra.nontrivial
   exact MvPolynomial.noZeroDivisors
 
+/- warning: mv_polynomial.map_mv_polynomial_eq_eval₂ -> MvPolynomial.map_mvPolynomial_eq_eval₂ is a dubious translation:
+lean 3 declaration is
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S (CommRing.toRing.{u3} S _inst_5)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> S) (RingHom.hasCoeToFun.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) ϕ p) (MvPolynomial.eval₂.{u1, u3, u2} R S σ (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u3} S _inst_5) (RingHom.comp.{u1, max u2 u1, u3} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) (fun (_x : RingHom.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> S) (RingHom.hasCoeToFun.{max u2 u1, u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toNonAssocRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_5)))) ϕ (MvPolynomial.X.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) s)) p)
+but is expected to have type
+  forall {R : Type.{u2}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] {S : Type.{u1}} [_inst_5 : CommRing.{u1} S] [_inst_6 : Finite.{succ u3} σ] (ϕ : RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) => S) p) (FunLike.coe.{max (max (succ u2) (succ u3)) 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R _inst_1)) S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u3) u1, max u2 u3, u1} (RingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{max u2 u3, u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) S (NonAssocRing.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toNonAssocRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toRing.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u2, u3} R σ _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))))) ϕ (MvPolynomial.X.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s)) p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂ₓ'. -/
 theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :
     ϕ p = MvPolynomial.eval₂ (ϕ.comp MvPolynomial.C) (fun s => ϕ (MvPolynomial.X s)) p :=
@@ -1174,6 +1538,12 @@ theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ :
   simp only [monomial_eq, ϕ.map_pow, ϕ.map_prod, ϕ.comp_apply, ϕ.map_mul, Finsupp.prod_pow]
 #align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂
 
+/- warning: mv_polynomial.mem_ideal_of_coeff_mem_ideal -> MvPolynomial.mem_ideal_of_coeff_mem_ideal is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)), (forall (m : Finsupp.{u2, 0} σ Nat Nat.hasZero), Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m p) (Ideal.comap.{u1, max u2 u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (RingHom.ringHomClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) -> (Membership.Mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) p I)
+but is expected to have type
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] (I : Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)), (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m p) (Ideal.comap.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) -> (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) p I)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_ideal_of_coeff_mem_ideal MvPolynomial.mem_ideal_of_coeff_mem_idealₓ'. -/
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself,
 multivariate version. -/
 theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPolynomial σ R)
@@ -1188,9 +1558,15 @@ theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPoly
   simpa [Ideal.mem_comap] using hcoe m
 #align mv_polynomial.mem_ideal_of_coeff_mem_ideal MvPolynomial.mem_ideal_of_coeff_mem_ideal
 
+/- warning: mv_polynomial.mem_map_C_iff -> MvPolynomial.mem_map_C_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Membership.Mem.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (SetLike.hasMem.{max u2 u1, max u2 u1} (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u2 u1, max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1)))))) f (Ideal.map.{u1, max u2 u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commRing.{u1, u2} R σ _inst_1))) (RingHom.ringHomClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) (forall (m : Finsupp.{u2, 0} σ Nat Nat.hasZero), Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m f) I)
+but is expected to have type
+  forall {R : Type.{u1}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Ideal.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Submodule.setLike.{max u1 u2, max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) (Semiring.toModule.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1)))))) f (Ideal.map.{u1, max u1 u2, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommRing.toRing.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.instCommRingMvPolynomialToCommSemiring.{u1, u2} R σ _inst_1))) (RingHom.instRingHomClassRingHom.{u1, max u1 u2} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) I)) (forall (m : Finsupp.{u2, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (MvPolynomial.coeff.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) m f) I)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_C_iffₓ'. -/
 /-- The push-forward of an ideal `I` of `R` to `mv_polynomial σ R` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
-theorem mem_map_c_iff {I : Ideal R} {f : MvPolynomial σ R} :
+theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
     f ∈ (Ideal.map (C : R →+* MvPolynomial σ R) I : Ideal (MvPolynomial σ R)) ↔
       ∀ m : σ →₀ ℕ, f.coeff m ∈ I :=
   by
@@ -1218,13 +1594,19 @@ theorem mem_map_c_iff {I : Ideal R} {f : MvPolynomial σ R} :
       exact Ideal.mul_mem_right _ _ this
     apply Ideal.mem_map_of_mem _
     exact hf m
-#align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_c_iff
-
+#align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_C_iff
+
+/- warning: mv_polynomial.ker_map -> MvPolynomial.ker_map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u3}} {σ : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u3} S] (f : RingHom.{u1, u3} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))), Eq.{succ (max u2 u1)} (Ideal.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.ker.{max u2 u1, max u2 u3, max (max u2 u1) u2 u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (RingHom.{max u2 u1, max u2 u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (MvPolynomial.commSemiring.{u3, u2} S σ (CommRing.toCommSemiring.{u3} S _inst_2))))) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (MvPolynomial.commSemiring.{u3, u2} S σ (CommRing.toCommSemiring.{u3} S _inst_2))) (RingHom.ringHomClass.{max u2 u1, max u2 u3} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u2, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_2)) (MvPolynomial.commSemiring.{u3, u2} S σ (CommRing.toCommSemiring.{u3} S _inst_2))))) (MvPolynomial.map.{u1, u3, u2} R S σ (CommRing.toCommSemiring.{u1} R _inst_1) (CommRing.toCommSemiring.{u3} S _inst_2) f)) (Ideal.map.{u1, max u2 u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.ringHomClass.{u1, max u2 u1} R (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (MvPolynomial.C.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.ker.{u1, u3, max u1 u3} R S (RingHom.{u1, u3} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u3} S (CommRing.toRing.{u3} S _inst_2)) (RingHom.ringHomClass.{u1, u3} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_2)))) f))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} {σ : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} S] (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))), Eq.{max (succ u2) (succ u3)} (Ideal.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.ker.{max u2 u3, max u3 u1, max (max u2 u3) u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))))) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))) (RingHom.instRingHomClassRingHom.{max u2 u3, max u3 u1} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_2)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_2))))) (MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_1) (CommRing.toCommSemiring.{u1} S _inst_2) f)) (Ideal.map.{u2, max u2 u3, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))) (RingHom.instRingHomClassRingHom.{u2, max u2 u3} R (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.C.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.ker.{u2, u1, max u2 u1} R S (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) f))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.ker_map MvPolynomial.ker_mapₓ'. -/
 theorem ker_map (f : R →+* S) :
     (map f : MvPolynomial σ R →+* MvPolynomial σ S).ker = f.ker.map (C : R →+* MvPolynomial σ R) :=
   by
   ext
-  rw [MvPolynomial.mem_map_c_iff, RingHom.mem_ker, MvPolynomial.ext_iff]
+  rw [MvPolynomial.mem_map_C_iff, RingHom.mem_ker, MvPolynomial.ext_iff]
   simp_rw [coeff_map, coeff_zero, RingHom.mem_ker]
 #align mv_polynomial.ker_map MvPolynomial.ker_map
 
@@ -1238,12 +1620,14 @@ open UniqueFactorizationMonoid
 
 namespace Polynomial
 
+#print Polynomial.uniqueFactorizationMonoid /-
 instance (priority := 100) uniqueFactorizationMonoid : UniqueFactorizationMonoid D[X] :=
   by
   haveI := Inhabited.default (NormalizationMonoid D)
   haveI := to_normalized_gcd_monoid D
   exact ufm_of_gcd_of_wfDvdMonoid
 #align polynomial.unique_factorization_monoid Polynomial.uniqueFactorizationMonoid
+-/
 
 end Polynomial
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -808,7 +808,7 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial
     induction' Fintype.card σ with d hd
     · exact (is_empty_alg_equiv R (Fin 0)).toMulEquiv.symm.prime_iff
     · rw [hd, ← Polynomial.prime_c_iff]
-      convert (finSuccEquiv R d).toMulEquiv.symm.prime_iff
+      convert(finSuccEquiv R d).toMulEquiv.symm.prime_iff
       rw [← fin_succ_equiv_comp_C_eq_C]
       rfl
 #align mv_polynomial.prime_C_iff_of_fintype mv_polynomial.prime_C_iff_of_fintype
@@ -828,7 +828,7 @@ theorem prime_c_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       rw [← algebra_map_eq] at hd
       have : algebraMap R _ r ∣ a' * b' :=
         by
-        convert (kill_compl Subtype.coe_injective).toRingHom.map_dvd hd
+        convert(kill_compl Subtype.coe_injective).toRingHom.map_dvd hd
         simpa
         simp
       rw [← rename_C (coe : s → σ)]

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -798,7 +798,7 @@ end Polynomial
 
 namespace MvPolynomial
 
-private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (c r : MvPolynomial σ R) ↔ Prime r :=
+private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   by
   rw [(rename_equiv R (Fintype.equivFin σ)).toMulEquiv.prime_iff]
   convert_to Prime (C r) ↔ _;
@@ -813,8 +813,8 @@ private theorem prime_C_iff_of_fintype [Fintype σ] : Prime (c r : MvPolynomial
       rfl
 #align mv_polynomial.prime_C_iff_of_fintype mv_polynomial.prime_C_iff_of_fintype
 
-theorem prime_c_iff : Prime (c r : MvPolynomial σ R) ↔ Prime r :=
-  ⟨comap_prime c constantCoeff (constantCoeff_c _), fun hr =>
+theorem prime_c_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
+  ⟨comap_prime C constantCoeff (constantCoeff_C _), fun hr =>
     ⟨fun h =>
       hr.1 <| by
         rw [← C_inj, h]
@@ -917,7 +917,7 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
       have hs2 : ∀ {x}, x ∈ I.degreeLe N → x ∈ Ideal.span (↑s : Set R[X]) :=
         hs ▸ fun x hx =>
           Submodule.span_induction hx (fun _ hx => Ideal.subset_span hx) (Ideal.zero_mem _)
-            (fun _ _ => Ideal.add_mem _) fun c f hf => f.c_mul' c ▸ Ideal.mul_mem_left _ _ hf
+            (fun _ _ => Ideal.add_mem _) fun c f hf => f.C_mul' c ▸ Ideal.mul_mem_left _ _ hf
       ⟨s,
         le_antisymm
             (Ideal.span_le.2 fun x hx =>
@@ -1164,7 +1164,7 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] : IsDomain (MvPoly
 
 theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :
-    ϕ p = MvPolynomial.eval₂ (ϕ.comp MvPolynomial.c) (fun s => ϕ (MvPolynomial.x s)) p :=
+    ϕ p = MvPolynomial.eval₂ (ϕ.comp MvPolynomial.C) (fun s => ϕ (MvPolynomial.X s)) p :=
   by
   cases nonempty_fintype σ
   refine' trans (congr_arg ϕ (MvPolynomial.as_sum p)) _
@@ -1177,7 +1177,7 @@ theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ :
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself,
 multivariate version. -/
 theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPolynomial σ R)
-    (hcoe : ∀ m : σ →₀ ℕ, p.coeff m ∈ I.comap (c : R →+* MvPolynomial σ R)) : p ∈ I :=
+    (hcoe : ∀ m : σ →₀ ℕ, p.coeff m ∈ I.comap (C : R →+* MvPolynomial σ R)) : p ∈ I :=
   by
   rw [as_sum p]
   suffices ∀ m ∈ p.support, monomial m (MvPolynomial.coeff m p) ∈ I by
@@ -1191,7 +1191,7 @@ theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPoly
 /-- The push-forward of an ideal `I` of `R` to `mv_polynomial σ R` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
 theorem mem_map_c_iff {I : Ideal R} {f : MvPolynomial σ R} :
-    f ∈ (Ideal.map (c : R →+* MvPolynomial σ R) I : Ideal (MvPolynomial σ R)) ↔
+    f ∈ (Ideal.map (C : R →+* MvPolynomial σ R) I : Ideal (MvPolynomial σ R)) ↔
       ∀ m : σ →₀ ℕ, f.coeff m ∈ I :=
   by
   constructor
@@ -1221,7 +1221,7 @@ theorem mem_map_c_iff {I : Ideal R} {f : MvPolynomial σ R} :
 #align mv_polynomial.mem_map_C_iff MvPolynomial.mem_map_c_iff
 
 theorem ker_map (f : R →+* S) :
-    (map f : MvPolynomial σ R →+* MvPolynomial σ S).ker = f.ker.map (c : R →+* MvPolynomial σ R) :=
+    (map f : MvPolynomial σ R →+* MvPolynomial σ S).ker = f.ker.map (C : R →+* MvPolynomial σ R) :=
   by
   ext
   rw [MvPolynomial.mem_map_c_iff, RingHom.mem_ker, MvPolynomial.ext_iff]

mathlib commit https://github.com/leanprover-community/mathlib/commit/f24cc2891c0e328f0ee8c57387103aa462c44b5e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.basic
-! leanprover-community/mathlib commit dfb0adb7c805b3f4fbfd283d16f71f7baccb88e6
+! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -699,128 +699,71 @@ section CommRing
 
 variable [CommRing R]
 
-theorem quotient_map_c_eq_zero {I : Ideal R} :
-    ∀ a ∈ I, ((Quotient.mk (map (C : R →+* R[X]) I : Ideal R[X])).comp C) a = 0 :=
-  by
-  intro a ha
-  rw [RingHom.comp_apply, quotient.eq_zero_iff_mem]
-  exact mem_map_of_mem _ ha
-#align ideal.quotient_map_C_eq_zero Ideal.quotient_map_c_eq_zero
-
-theorem eval₂_c_mk_eq_zero {I : Ideal R} :
-    ∀ f ∈ (map (C : R →+* R[X]) I : Ideal R[X]), eval₂RingHom (C.comp (Quotient.mk I)) X f = 0 :=
-  by
-  intro a ha
-  rw [← sum_monomial_eq a]
-  dsimp
-  rw [eval₂_sum]
-  refine' Finset.sum_eq_zero fun n hn => _
-  dsimp
-  rw [eval₂_monomial (C.comp (Quotient.mk' I)) X]
-  refine' mul_eq_zero_of_left (Polynomial.ext fun m => _) (X ^ n)
-  erw [coeff_C]
-  by_cases h : m = 0
-  · simpa [h] using quotient.eq_zero_iff_mem.2 ((mem_map_C_iff.1 ha) n)
-  · simp [h]
-#align ideal.eval₂_C_mk_eq_zero Ideal.eval₂_c_mk_eq_zero
-
-/-- If `I` is an ideal of `R`, then the ring polynomials over the quotient ring `I.quotient` is
-isomorphic to the quotient of `R[X]` by the ideal `map C I`,
-where `map C I` contains exactly the polynomials whose coefficients all lie in `I` -/
-def polynomialQuotientEquivQuotientPolynomial (I : Ideal R) :
-    (R ⧸ I)[X] ≃+* R[X] ⧸ (map C I : Ideal R[X])
-    where
-  toFun :=
-    eval₂RingHom
-      (Quotient.lift I ((Quotient.mk (map C I : Ideal R[X])).comp C) quotient_map_c_eq_zero)
-      (Quotient.mk (map C I : Ideal R[X]) X)
-  invFun :=
-    Quotient.lift (map C I : Ideal R[X]) (eval₂RingHom (C.comp (Quotient.mk I)) X)
-      eval₂_c_mk_eq_zero
-  map_mul' f g := by simp only [coe_eval₂_ring_hom, eval₂_mul]
-  map_add' f g := by simp only [eval₂_add, coe_eval₂_ring_hom]
-  left_inv := by
-    intro f
-    apply Polynomial.induction_on' f
-    · intro p q hp hq
-      simp only [coe_eval₂_ring_hom] at hp
-      simp only [coe_eval₂_ring_hom] at hq
-      simp only [coe_eval₂_ring_hom, hp, hq, RingHom.map_add]
-    · rintro n ⟨x⟩
-      simp only [← smul_X_eq_monomial, C_mul', Quotient.lift_mk, Submodule.Quotient.quot_mk_eq_mk,
-        quotient.mk_eq_mk, eval₂_X_pow, eval₂_smul, coe_eval₂_ring_hom, RingHom.map_pow, eval₂_C,
-        RingHom.coe_comp, RingHom.map_mul, eval₂_X]
-  right_inv := by
-    rintro ⟨f⟩
-    apply Polynomial.induction_on' f
-    · simp_intro p q hp hq
-      rw [hp, hq]
-    · intro n a
-      simp only [← smul_X_eq_monomial, ← C_mul' a (X ^ n), Quotient.lift_mk,
-        Submodule.Quotient.quot_mk_eq_mk, quotient.mk_eq_mk, eval₂_X_pow, eval₂_smul,
-        coe_eval₂_ring_hom, RingHom.map_pow, eval₂_C, RingHom.coe_comp, RingHom.map_mul, eval₂_X]
-#align ideal.polynomial_quotient_equiv_quotient_polynomial Ideal.polynomialQuotientEquivQuotientPolynomial
-
-@[simp]
-theorem polynomialQuotientEquivQuotientPolynomial_symm_mk (I : Ideal R) (f : R[X]) :
-    I.polynomialQuotientEquivQuotientPolynomial.symm (Quotient.mk _ f) = f.map (Quotient.mk I) := by
-  rw [polynomial_quotient_equiv_quotient_polynomial, RingEquiv.symm_mk, [anonymous],
-    Ideal.Quotient.lift_mk, coe_eval₂_ring_hom, eval₂_eq_eval_map, ← Polynomial.map_map, ←
-    eval₂_eq_eval_map, Polynomial.eval₂_C_X]
-#align ideal.polynomial_quotient_equiv_quotient_polynomial_symm_mk Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk
-
-@[simp]
-theorem polynomialQuotientEquivQuotientPolynomial_map_mk (I : Ideal R) (f : R[X]) :
-    I.polynomialQuotientEquivQuotientPolynomial (f.map I.Quotient.mk) = Quotient.mk _ f :=
+/-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
+theorem isPrime_map_c_iff_isPrime (P : Ideal R) :
+    IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) ↔ IsPrime P :=
   by
-  apply (polynomial_quotient_equiv_quotient_polynomial I).symm.Injective
-  rw [RingEquiv.symm_apply_apply, polynomial_quotient_equiv_quotient_polynomial_symm_mk]
-#align ideal.polynomial_quotient_equiv_quotient_polynomial_map_mk Ideal.polynomialQuotientEquivQuotientPolynomial_map_mk
-
-/-- If `P` is a prime ideal of `R`, then `R[x]/(P)` is an integral domain. -/
-theorem isDomain_map_c_quotient {P : Ideal R} (H : IsPrime P) :
-    IsDomain (R[X] ⧸ (map (C : R →+* R[X]) P : Ideal R[X])) :=
-  RingEquiv.isDomain (Polynomial (R ⧸ P)) (polynomialQuotientEquivQuotientPolynomial P).symm
-#align ideal.is_domain_map_C_quotient Ideal.isDomain_map_c_quotient
+  -- Porting note: the following proof avoids quotient rings
+  -- It can be golfed substantially by using something like
+  -- `(quotient.is_domain_iff_prime (map C P : ideal R[X]))`
+  constructor
+  · intro H
+    have := @comap_is_prime R R[X] (R →+* R[X]) _ _ _ C (map C P) H
+    convert this using 1
+    ext x
+    simp only [mem_comap, mem_map_C_iff]
+    constructor
+    · rintro h (- | n)
+      · simpa only [coeff_C_zero] using h
+      · simp only [coeff_C_ne_zero (Nat.succ_ne_zero _), Submodule.zero_mem]
+    · intro h
+      simpa only [coeff_C_zero] using h 0
+  · intro h
+    constructor
+    · rw [Ne.def, eq_top_iff_one, mem_map_C_iff, not_forall]
+      use 0
+      rw [coeff_one_zero, ← eq_top_iff_one]
+      exact h.1
+    · intro f g
+      simp only [mem_map_C_iff]
+      contrapose!
+      rintro ⟨hf, hg⟩
+      classical
+        let m := Nat.find hf
+        let n := Nat.find hg
+        refine' ⟨m + n, _⟩
+        rw [coeff_mul, ← Finset.insert_erase ((@Finset.Nat.mem_antidiagonal _ (m, n)).mpr rfl),
+          Finset.sum_insert (Finset.not_mem_erase _ _), (P.add_mem_iff_left _).Not]
+        · apply mt h.2
+          rw [not_or]
+          exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
+        apply P.sum_mem
+        rintro ⟨i, j⟩ hij
+        rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij
+        simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij
+        obtain hi | hj : i < m ∨ j < n :=
+          by
+          rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
+          rintro (hmi | rfl)
+          · rw [← not_le]
+            intro hnj
+            exact (add_lt_add_of_lt_of_le hmi hnj).Ne hij.2.symm
+          ·
+            simpa only [eq_self_iff_true, not_true, false_or_iff, add_right_inj,
+              not_and_self_iff] using hij
+        · rw [mul_comm]
+          apply P.mul_mem_left
+          exact Classical.not_not.1 (Nat.find_min hf hi)
+        · apply P.mul_mem_left
+          exact Classical.not_not.1 (Nat.find_min hg hj)
+#align ideal.is_prime_map_C_iff_is_prime Ideal.isPrime_map_c_iff_isPrime
 
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_c_of_isPrime {P : Ideal R} (H : IsPrime P) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) :=
-  (Quotient.isDomain_iff_prime (map C P : Ideal R[X])).mp (isDomain_map_c_quotient H)
+  (isPrime_map_c_iff_isPrime P).mpr H
 #align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_c_of_isPrime
 
-/-- Given any ring `R` and an ideal `I` of `R[X]`, we get a map `R → R[x] → R[x]/I`.
-  If we let `R` be the image of `R` in `R[x]/I` then we also have a map `R[x] → R'[x]`.
-  In particular we can map `I` across this map, to get `I'` and a new map `R' → R'[x] → R'[x]/I`.
-  This theorem shows `I'` will not contain any non-zero constant polynomials
-  -/
-theorem eq_zero_of_polynomial_mem_map_range (I : Ideal R[X]) (x : ((Quotient.mk I).comp C).range)
-    (hx : C x ∈ I.map (Polynomial.mapRingHom ((Quotient.mk I).comp C).range_restrict)) : x = 0 :=
-  by
-  let i := ((Quotient.mk' I).comp C).range_restrict
-  have hi' : (Polynomial.mapRingHom i).ker ≤ I :=
-    by
-    refine' fun f hf => polynomial_mem_ideal_of_coeff_mem_ideal I f fun n => _
-    rw [mem_comap, ← quotient.eq_zero_iff_mem, ← RingHom.comp_apply]
-    rw [RingHom.mem_ker, coe_map_ring_hom] at hf
-    replace hf := congr_arg (fun f : Polynomial _ => f.coeff n) hf
-    simp only [coeff_map, coeff_zero] at hf
-    rwa [Subtype.ext_iff, RingHom.coe_rangeRestrict] at hf
-  obtain ⟨x, hx'⟩ := x
-  obtain ⟨y, rfl⟩ := RingHom.mem_range.1 hx'
-  refine' Subtype.eq _
-  simp only [RingHom.comp_apply, quotient.eq_zero_iff_mem, ZeroMemClass.coe_zero,
-    Subtype.val_eq_coe]
-  suffices C (i y) ∈ I.map (Polynomial.mapRingHom i)
-    by
-    obtain ⟨f, hf⟩ :=
-      mem_image_of_mem_map_of_surjective (Polynomial.mapRingHom i)
-        (Polynomial.map_surjective _ ((Quotient.mk' I).comp C).rangeRestrict_surjective) this
-    refine' sub_add_cancel (C y) f ▸ I.add_mem (hi' _ : C y - f ∈ I) hf.1
-    rw [RingHom.mem_ker, RingHom.map_sub, hf.2, sub_eq_zero, coe_map_ring_hom, map_C]
-  exact hx
-#align ideal.eq_zero_of_polynomial_mem_map_range Ideal.eq_zero_of_polynomial_mem_map_range
-
 theorem is_fg_degreeLe [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
     Submodule.Fg (I.degreeLe n) :=
   isNoetherian_submodule_left.1
@@ -1231,15 +1174,6 @@ theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ :
   simp only [monomial_eq, ϕ.map_pow, ϕ.map_prod, ϕ.comp_apply, ϕ.map_mul, Finsupp.prod_pow]
 #align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂
 
-theorem quotient_map_c_eq_zero {I : Ideal R} {i : R} (hi : i ∈ I) :
-    (Ideal.Quotient.mk (Ideal.map (c : R →+* MvPolynomial σ R) I : Ideal (MvPolynomial σ R))).comp c
-        i =
-      0 :=
-  by
-  simp only [Function.comp_apply, RingHom.coe_comp, Ideal.Quotient.eq_zero_iff_mem]
-  exact Ideal.mem_map_of_mem _ hi
-#align mv_polynomial.quotient_map_C_eq_zero MvPolynomial.quotient_map_c_eq_zero
-
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself,
 multivariate version. -/
 theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPolynomial σ R)
@@ -1294,65 +1228,6 @@ theorem ker_map (f : R →+* S) :
   simp_rw [coeff_map, coeff_zero, RingHom.mem_ker]
 #align mv_polynomial.ker_map MvPolynomial.ker_map
 
-theorem eval₂_c_mk_eq_zero {I : Ideal R} {a : MvPolynomial σ R}
-    (ha : a ∈ (Ideal.map (c : R →+* MvPolynomial σ R) I : Ideal (MvPolynomial σ R))) :
-    eval₂Hom (c.comp (Ideal.Quotient.mk I)) x a = 0 :=
-  by
-  rw [as_sum a]
-  rw [coe_eval₂_hom, eval₂_sum]
-  refine' Finset.sum_eq_zero fun n hn => _
-  simp only [eval₂_monomial, Function.comp_apply, RingHom.coe_comp]
-  refine' mul_eq_zero_of_left _ _
-  suffices coeff n a ∈ I by
-    rw [← @Ideal.mk_ker R _ I, RingHom.mem_ker] at this
-    simp only [this, C_0]
-  exact mem_map_C_iff.1 ha n
-#align mv_polynomial.eval₂_C_mk_eq_zero MvPolynomial.eval₂_c_mk_eq_zero
-
-/-- If `I` is an ideal of `R`, then the ring `mv_polynomial σ I.quotient` is isomorphic as an
-`R`-algebra to the quotient of `mv_polynomial σ R` by the ideal generated by `I`. -/
-def quotientEquivQuotientMvPolynomial (I : Ideal R) :
-    MvPolynomial σ (R ⧸ I) ≃ₐ[R] MvPolynomial σ R ⧸ (Ideal.map c I : Ideal (MvPolynomial σ R))
-    where
-  toFun :=
-    eval₂Hom
-      (Ideal.Quotient.lift I ((Ideal.Quotient.mk (Ideal.map c I : Ideal (MvPolynomial σ R))).comp c)
-        fun i hi => quotient_map_c_eq_zero hi)
-      fun i => Ideal.Quotient.mk (Ideal.map c I : Ideal (MvPolynomial σ R)) (x i)
-  invFun :=
-    Ideal.Quotient.lift (Ideal.map c I : Ideal (MvPolynomial σ R))
-      (eval₂Hom (c.comp (Ideal.Quotient.mk I)) x) fun a ha => eval₂_c_mk_eq_zero ha
-  map_mul' := RingHom.map_mul _
-  map_add' := RingHom.map_add _
-  left_inv := by
-    intro f
-    apply induction_on f
-    · rintro ⟨r⟩
-      rw [coe_eval₂_hom, eval₂_C]
-      simp only [eval₂_hom_eq_bind₂, Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.lift_mk,
-        Ideal.Quotient.mk_eq_mk, bind₂_C_right, RingHom.coe_comp]
-    · simp_intro p q hp hq only [RingHom.map_add, MvPolynomial.coe_eval₂Hom, coe_eval₂_hom,
-        MvPolynomial.eval₂_add, MvPolynomial.eval₂Hom_eq_bind₂, eval₂_hom_eq_bind₂]
-      rw [hp, hq]
-    · simp_intro p i hp only [eval₂_hom_eq_bind₂, coe_eval₂_hom]
-      simp only [hp, eval₂_hom_eq_bind₂, coe_eval₂_hom, Ideal.Quotient.lift_mk, bind₂_X_right,
-        eval₂_mul, RingHom.map_mul, eval₂_X]
-  right_inv := by
-    rintro ⟨f⟩
-    apply induction_on f
-    · intro r
-      simp only [Submodule.Quotient.quot_mk_eq_mk, Ideal.Quotient.lift_mk, Ideal.Quotient.mk_eq_mk,
-        RingHom.coe_comp, eval₂_hom_C]
-    · simp_intro p q hp hq only [eval₂_hom_eq_bind₂, Submodule.Quotient.quot_mk_eq_mk, eval₂_add,
-        RingHom.map_add, coe_eval₂_hom, Ideal.Quotient.lift_mk, Ideal.Quotient.mk_eq_mk]
-      rw [hp, hq]
-    · simp_intro p i hp only [eval₂_hom_eq_bind₂, Submodule.Quotient.quot_mk_eq_mk, coe_eval₂_hom,
-        Ideal.Quotient.lift_mk, Ideal.Quotient.mk_eq_mk, bind₂_X_right, eval₂_mul, RingHom.map_mul,
-        eval₂_X]
-      simp only [hp]
-  commutes' r := eval₂Hom_c _ _ (Ideal.Quotient.mk I r)
-#align mv_polynomial.quotient_equiv_quotient_mv_polynomial MvPolynomial.quotientEquivQuotientMvPolynomial
-
 end MvPolynomial
 
 section UniqueFactorizationDomain

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

@@ -175,7 +175,7 @@ theorem eval_eq_sum_degreeLtEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n)
     p.eval x = ∑ i, degreeLtEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) :=
   by
   simp_rw [eval_eq_sum]
-  exact (sum_fin _ (by simp_rw [zero_mul, forall_const]) (mem_degree_lt.mp hp)).symm
+  exact (sum_fin _ (by simp_rw [MulZeroClass.zero_mul, forall_const]) (mem_degree_lt.mp hp)).symm
 #align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLtEquiv
 
 /-- The finset of nonzero coefficients of a polynomial. -/
@@ -676,7 +676,7 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
   obtain ⟨p, hp⟩ := hR.mul_inv_cancel X_ne_zero
   have hp0 : p ≠ 0 := by
     rintro rfl
-    rw [mul_zero] at hp
+    rw [MulZeroClass.mul_zero] at hp
     exact zero_ne_one hp
   have := degree_lt_degree_mul_X hp0
   rw [← X_mul, congr_arg degree hp, degree_one, Nat.WithBot.lt_zero_iff, degree_eq_bot] at this
@@ -1002,7 +1002,7 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
               apply hp0
               ext i
               refine' (mul_one _).symm.trans _
-              rw [← h, mul_zero]
+              rw [← h, MulZeroClass.mul_zero]
               rfl
             haveI : Nontrivial R := ⟨⟨0, 1, this⟩⟩
             have : p.leading_coeff ∈ I.leading_coeff_nth N :=

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

@@ -766,7 +766,7 @@ theorem polynomialQuotientEquivQuotientPolynomial_symm_mk (I : Ideal R) (f : R[X
     I.polynomialQuotientEquivQuotientPolynomial.symm (Quotient.mk _ f) = f.map (Quotient.mk I) := by
   rw [polynomial_quotient_equiv_quotient_polynomial, RingEquiv.symm_mk, [anonymous],
     Ideal.Quotient.lift_mk, coe_eval₂_ring_hom, eval₂_eq_eval_map, ← Polynomial.map_map, ←
-    eval₂_eq_eval_map, Polynomial.eval₂_c_x]
+    eval₂_eq_eval_map, Polynomial.eval₂_C_X]
 #align ideal.polynomial_quotient_equiv_quotient_polynomial_symm_mk Ideal.polynomialQuotientEquivQuotientPolynomial_symm_mk
 
 @[simp]
@@ -842,7 +842,7 @@ variable (σ) {r : R}
 namespace Polynomial
 
 theorem prime_c_iff : Prime (C r) ↔ Prime r :=
-  ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_c, fun hr =>
+  ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr =>
     by
     have := hr.1
     rw [← Ideal.span_singleton_prime] at hr⊢

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

@@ -611,7 +611,7 @@ theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :
     ⟨fun ⟨p, hpI, hpdeg, hpx⟩ => by
       rwa [← hpx, Polynomial.leadingCoeff,
         Nat.eq_zero_of_le_zero (nat_degree_le_of_degree_le hpdeg), ← eq_C_of_degree_le_zero hpdeg],
-      fun hx => ⟨C x, hx, degree_c_le, leadingCoeff_c x⟩⟩
+      fun hx => ⟨C x, hx, degree_C_le, leadingCoeff_C x⟩⟩
 #align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zero
 
 theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤ I.leadingCoeffNth n :=
@@ -944,7 +944,7 @@ instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R
       · simp only [hdeg, add_zero]
         refine' Prod.Lex.right _ ⟨_, ⟨c.leading_coeff, fun unit_c => not_unit_c _, rfl⟩⟩
         · rwa [Ne, Polynomial.leadingCoeff_eq_zero]
-        rw [Polynomial.isUnit_iff, Polynomial.eq_c_of_degree_eq_zero hdeg]
+        rw [Polynomial.isUnit_iff, Polynomial.eq_C_of_degree_eq_zero hdeg]
         use c.leading_coeff, unit_c
         rw [Polynomial.leadingCoeff, Polynomial.natDegree_eq_of_degree_eq_some hdeg]
       · apply Prod.Lex.left
@@ -1021,14 +1021,14 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
               exact hp0 H
             have h1 : p.degree = (q * Polynomial.X ^ (k - q.nat_degree)).degree :=
               by
-              rw [Polynomial.degree_mul', Polynomial.degree_x_pow]
+              rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
               rw [Polynomial.degree_eq_natDegree hp0, Polynomial.degree_eq_natDegree hq0]
               rw [← WithBot.coe_add, add_tsub_cancel_of_le, hn]
               · refine' le_trans (Polynomial.natDegree_le_of_degree_le hdq) (le_of_lt h)
-              rw [Polynomial.leadingCoeff_x_pow, mul_one]
+              rw [Polynomial.leadingCoeff_X_pow, mul_one]
               exact mt Polynomial.leadingCoeff_eq_zero.1 hq0
             have h2 : p.leading_coeff = (q * Polynomial.X ^ (k - q.nat_degree)).leadingCoeff := by
-              rw [← hlqp, Polynomial.leadingCoeff_mul_x_pow]
+              rw [← hlqp, Polynomial.leadingCoeff_mul_X_pow]
             have := Polynomial.degree_sub_lt h1 hp0 h2
             rw [Polynomial.degree_eq_natDegree hp0] at this
             rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.nat_degree))]

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

@@ -75,7 +75,7 @@ theorem degreeLe_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLe R m ≤ degre
 #align polynomial.degree_le_mono Polynomial.degreeLe_mono
 
 theorem degreeLe_eq_span_x_pow {n : ℕ} :
-    degreeLe R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (x : R[X]) ^ n) :=
+    degreeLe R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) :=
   by
   apply le_antisymm
   · intro p hp
@@ -110,7 +110,7 @@ theorem degreeLt_mono {m n : ℕ} (H : m ≤ n) : degreeLt R m ≤ degreeLt R n
 #align polynomial.degree_lt_mono Polynomial.degreeLt_mono
 
 theorem degreeLt_eq_span_x_pow {n : ℕ} :
-    degreeLt R n = Submodule.span R ↑((Finset.range n).image fun n => x ^ n : Finset R[X]) :=
+    degreeLt R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) :=
   by
   apply le_antisymm
   · intro p hp
@@ -207,8 +207,8 @@ theorem coeff_mem_frange (p : R[X]) (n : ℕ) (h : p.coeff n ≠ 0) : p.coeff n
 #align polynomial.coeff_mem_frange Polynomial.coeff_mem_frange
 
 theorem geom_sum_x_comp_x_add_one_eq_sum (n : ℕ) :
-    (∑ i in range n, (x : R[X]) ^ i).comp (x + 1) =
-      (Finset.range n).Sum fun i : ℕ => (n.choose (i + 1) : R[X]) * x ^ i :=
+    (∑ i in range n, (X : R[X]) ^ i).comp (X + 1) =
+      (Finset.range n).Sum fun i : ℕ => (n.choose (i + 1) : R[X]) * X ^ i :=
   by
   ext i
   trans (n.choose (i + 1) : R); swap
@@ -247,7 +247,7 @@ theorem Monic.geom_sum' {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.degree) {n : ℕ
   hP.geom_sum (natDegree_pos_iff_degree_pos.2 hdeg) hn
 #align polynomial.monic.geom_sum' Polynomial.Monic.geom_sum'
 
-theorem monic_geom_sum_x {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (x : R[X]) ^ i).Monic :=
+theorem monic_geom_sum_x {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (X : R[X]) ^ i).Monic :=
   by
   nontriviality R
   apply monic_X.geom_sum _ hn
@@ -540,14 +540,14 @@ variable [CommSemiring R] [Semiring S]
 
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself -/
 theorem polynomial_mem_ideal_of_coeff_mem_ideal (I : Ideal R[X]) (p : R[X])
-    (hp : ∀ n : ℕ, p.coeff n ∈ I.comap (c : R →+* R[X])) : p ∈ I :=
-  sum_c_mul_x_pow_eq p ▸ Submodule.sum_mem I fun n hn => I.mul_mem_right _ (hp n)
+    (hp : ∀ n : ℕ, p.coeff n ∈ I.comap (C : R →+* R[X])) : p ∈ I :=
+  sum_C_mul_X_pow_eq p ▸ Submodule.sum_mem I fun n hn => I.mul_mem_right _ (hp n)
 #align ideal.polynomial_mem_ideal_of_coeff_mem_ideal Ideal.polynomial_mem_ideal_of_coeff_mem_ideal
 
 /-- The push-forward of an ideal `I` of `R` to `R[X]` via inclusion
  is exactly the set of polynomials whose coefficients are in `I` -/
 theorem mem_map_c_iff {I : Ideal R} {f : R[X]} :
-    f ∈ (Ideal.map (c : R →+* R[X]) I : Ideal R[X]) ↔ ∀ n : ℕ, f.coeff n ∈ I :=
+    f ∈ (Ideal.map (C : R →+* R[X]) I : Ideal R[X]) ↔ ∀ n : ℕ, f.coeff n ∈ I :=
   by
   constructor
   · intro hf
@@ -572,7 +572,7 @@ theorem mem_map_c_iff {I : Ideal R} {f : R[X]} :
 #align ideal.mem_map_C_iff Ideal.mem_map_c_iff
 
 theorem Polynomial.ker_mapRingHom (f : R →+* S) :
-    (Polynomial.mapRingHom f).ker = f.ker.map (c : R →+* R[X]) :=
+    (Polynomial.mapRingHom f).ker = f.ker.map (C : R →+* R[X]) :=
   by
   ext
   rw [mem_map_C_iff, RingHom.mem_ker, Polynomial.ext_iff]
@@ -606,12 +606,12 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
     · rw [Polynomial.leadingCoeff, ← coeff_mul_X_pow p (n - nat_degree p), this]
 #align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNth
 
-theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ c x ∈ I :=
+theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :=
   (mem_leadingCoeffNth _ _ _).trans
     ⟨fun ⟨p, hpI, hpdeg, hpx⟩ => by
       rwa [← hpx, Polynomial.leadingCoeff,
         Nat.eq_zero_of_le_zero (nat_degree_le_of_degree_le hpdeg), ← eq_C_of_degree_le_zero hpdeg],
-      fun hx => ⟨c x, hx, degree_c_le, leadingCoeff_c x⟩⟩
+      fun hx => ⟨C x, hx, degree_c_le, leadingCoeff_c x⟩⟩
 #align ideal.mem_leading_coeff_nth_zero Ideal.mem_leadingCoeffNth_zero
 
 theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤ I.leadingCoeffNth n :=
@@ -685,7 +685,7 @@ theorem polynomial_not_isField : ¬IsField R[X] :=
 
 /-- The only constant in a maximal ideal over a field is `0`. -/
 theorem eq_zero_of_constant_mem_of_maximal (hR : IsField R) (I : Ideal R[X]) [hI : I.IsMaximal]
-    (x : R) (hx : c x ∈ I) : x = 0 :=
+    (x : R) (hx : C x ∈ I) : x = 0 :=
   by
   refine' by_contradiction fun hx0 => hI.ne_top ((eq_top_iff_one I).2 _)
   obtain ⟨y, hy⟩ := hR.mul_inv_cancel hx0
@@ -700,7 +700,7 @@ section CommRing
 variable [CommRing R]
 
 theorem quotient_map_c_eq_zero {I : Ideal R} :
-    ∀ a ∈ I, ((Quotient.mk (map (c : R →+* R[X]) I : Ideal R[X])).comp c) a = 0 :=
+    ∀ a ∈ I, ((Quotient.mk (map (C : R →+* R[X]) I : Ideal R[X])).comp C) a = 0 :=
   by
   intro a ha
   rw [RingHom.comp_apply, quotient.eq_zero_iff_mem]
@@ -708,7 +708,7 @@ theorem quotient_map_c_eq_zero {I : Ideal R} :
 #align ideal.quotient_map_C_eq_zero Ideal.quotient_map_c_eq_zero
 
 theorem eval₂_c_mk_eq_zero {I : Ideal R} :
-    ∀ f ∈ (map (c : R →+* R[X]) I : Ideal R[X]), eval₂RingHom (c.comp (Quotient.mk I)) x f = 0 :=
+    ∀ f ∈ (map (C : R →+* R[X]) I : Ideal R[X]), eval₂RingHom (C.comp (Quotient.mk I)) X f = 0 :=
   by
   intro a ha
   rw [← sum_monomial_eq a]
@@ -728,14 +728,14 @@ theorem eval₂_c_mk_eq_zero {I : Ideal R} :
 isomorphic to the quotient of `R[X]` by the ideal `map C I`,
 where `map C I` contains exactly the polynomials whose coefficients all lie in `I` -/
 def polynomialQuotientEquivQuotientPolynomial (I : Ideal R) :
-    (R ⧸ I)[X] ≃+* R[X] ⧸ (map c I : Ideal R[X])
+    (R ⧸ I)[X] ≃+* R[X] ⧸ (map C I : Ideal R[X])
     where
   toFun :=
     eval₂RingHom
-      (Quotient.lift I ((Quotient.mk (map c I : Ideal R[X])).comp c) quotient_map_c_eq_zero)
-      (Quotient.mk (map c I : Ideal R[X]) x)
+      (Quotient.lift I ((Quotient.mk (map C I : Ideal R[X])).comp C) quotient_map_c_eq_zero)
+      (Quotient.mk (map C I : Ideal R[X]) X)
   invFun :=
-    Quotient.lift (map c I : Ideal R[X]) (eval₂RingHom (c.comp (Quotient.mk I)) x)
+    Quotient.lift (map C I : Ideal R[X]) (eval₂RingHom (C.comp (Quotient.mk I)) X)
       eval₂_c_mk_eq_zero
   map_mul' f g := by simp only [coe_eval₂_ring_hom, eval₂_mul]
   map_add' f g := by simp only [eval₂_add, coe_eval₂_ring_hom]
@@ -779,14 +779,14 @@ theorem polynomialQuotientEquivQuotientPolynomial_map_mk (I : Ideal R) (f : R[X]
 
 /-- If `P` is a prime ideal of `R`, then `R[x]/(P)` is an integral domain. -/
 theorem isDomain_map_c_quotient {P : Ideal R} (H : IsPrime P) :
-    IsDomain (R[X] ⧸ (map (c : R →+* R[X]) P : Ideal R[X])) :=
+    IsDomain (R[X] ⧸ (map (C : R →+* R[X]) P : Ideal R[X])) :=
   RingEquiv.isDomain (Polynomial (R ⧸ P)) (polynomialQuotientEquivQuotientPolynomial P).symm
 #align ideal.is_domain_map_C_quotient Ideal.isDomain_map_c_quotient
 
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_c_of_isPrime {P : Ideal R} (H : IsPrime P) :
-    IsPrime (map (c : R →+* R[X]) P : Ideal R[X]) :=
-  (Quotient.isDomain_iff_prime (map c P : Ideal R[X])).mp (isDomain_map_c_quotient H)
+    IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) :=
+  (Quotient.isDomain_iff_prime (map C P : Ideal R[X])).mp (isDomain_map_c_quotient H)
 #align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_c_of_isPrime
 
 /-- Given any ring `R` and an ideal `I` of `R[X]`, we get a map `R → R[x] → R[x]/I`.
@@ -794,8 +794,8 @@ theorem isPrime_map_c_of_isPrime {P : Ideal R} (H : IsPrime P) :
   In particular we can map `I` across this map, to get `I'` and a new map `R' → R'[x] → R'[x]/I`.
   This theorem shows `I'` will not contain any non-zero constant polynomials
   -/
-theorem eq_zero_of_polynomial_mem_map_range (I : Ideal R[X]) (x : ((Quotient.mk I).comp c).range)
-    (hx : c x ∈ I.map (Polynomial.mapRingHom ((Quotient.mk I).comp c).range_restrict)) : x = 0 :=
+theorem eq_zero_of_polynomial_mem_map_range (I : Ideal R[X]) (x : ((Quotient.mk I).comp C).range)
+    (hx : C x ∈ I.map (Polynomial.mapRingHom ((Quotient.mk I).comp C).range_restrict)) : x = 0 :=
   by
   let i := ((Quotient.mk' I).comp C).range_restrict
   have hi' : (Polynomial.mapRingHom i).ker ≤ I :=
@@ -841,8 +841,8 @@ variable (σ) {r : R}
 
 namespace Polynomial
 
-theorem prime_c_iff : Prime (c r) ↔ Prime r :=
-  ⟨comap_prime c (evalRingHom (0 : R)) fun r => eval_c, fun hr =>
+theorem prime_c_iff : Prime (C r) ↔ Prime r :=
+  ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_c, fun hr =>
     by
     have := hr.1
     rw [← Ideal.span_singleton_prime] at hr⊢
@@ -1019,7 +1019,7 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
               rw [← Polynomial.leadingCoeff_eq_zero] at H
               rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H
               exact hp0 H
-            have h1 : p.degree = (q * Polynomial.x ^ (k - q.nat_degree)).degree :=
+            have h1 : p.degree = (q * Polynomial.X ^ (k - q.nat_degree)).degree :=
               by
               rw [Polynomial.degree_mul', Polynomial.degree_x_pow]
               rw [Polynomial.degree_eq_natDegree hp0, Polynomial.degree_eq_natDegree hq0]
@@ -1027,13 +1027,13 @@ protected theorem Polynomial.isNoetherianRing [IsNoetherianRing R] : IsNoetheria
               · refine' le_trans (Polynomial.natDegree_le_of_degree_le hdq) (le_of_lt h)
               rw [Polynomial.leadingCoeff_x_pow, mul_one]
               exact mt Polynomial.leadingCoeff_eq_zero.1 hq0
-            have h2 : p.leading_coeff = (q * Polynomial.x ^ (k - q.nat_degree)).leadingCoeff := by
+            have h2 : p.leading_coeff = (q * Polynomial.X ^ (k - q.nat_degree)).leadingCoeff := by
               rw [← hlqp, Polynomial.leadingCoeff_mul_x_pow]
             have := Polynomial.degree_sub_lt h1 hp0 h2
             rw [Polynomial.degree_eq_natDegree hp0] at this
-            rw [← sub_add_cancel p (q * Polynomial.x ^ (k - q.nat_degree))]
+            rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.nat_degree))]
             refine' (Ideal.span ↑s).add_mem _ ((Ideal.span ↑s).mul_mem_right _ _)
-            · by_cases hpq : p - q * Polynomial.x ^ (k - q.nat_degree) = 0
+            · by_cases hpq : p - q * Polynomial.X ^ (k - q.nat_degree) = 0
               · rw [hpq]
                 exact Ideal.zero_mem _
               refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.basic
-! leanprover-community/mathlib commit b1d911acd60ab198808e853292106ee352b648ea
+! leanprover-community/mathlib commit dfb0adb7c805b3f4fbfd283d16f71f7baccb88e6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1133,7 +1133,7 @@ theorem sup_ker_aeval_eq_ker_aeval_mul_of_coprime (f : M →ₗ[R] M) {p q : R[X
     ⟨aeval f (q * q') v, LinearMap.mem_ker.1 h_eval₂_pqq', aeval f (p * p') v,
       LinearMap.mem_ker.1 h_eval₂_qpp', _⟩
   rw [add_comm, mul_comm p p', mul_comm q q']
-  simpa using congr_arg (fun p : R[X] => aeval f p v) hpq'
+  simpa only [map_add, map_mul, aeval_one] using congr_arg (fun p : R[X] => aeval f p v) hpq'
 #align polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime
 
 end Polynomial

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

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

@@ -101,7 +101,7 @@ theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n
   rw [degree, Finset.max_eq_sup_coe]
   rw [Finset.sup_lt_iff ?_]
   rotate_left
-  apply WithBot.bot_lt_coe
+  · apply WithBot.bot_lt_coe
   conv_rhs =>
     simp only [mem_support_iff]
     intro b
@@ -673,8 +673,8 @@ theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤
 
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x := by
   rw [leadingCoeff, Submodule.mem_iSup_of_directed]
-  simp only [mem_leadingCoeffNth]
-  · constructor
+  · simp only [mem_leadingCoeffNth]
+    constructor
     · rintro ⟨i, p, hpI, _, rfl⟩
       exact ⟨p, hpI, rfl⟩
     rintro ⟨p, hpI, rfl⟩
@@ -998,9 +998,9 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
             exact hp0 H
           have h1 : p.degree = (q * Polynomial.X ^ (k - q.natDegree)).degree := by
             rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
-            rw [Polynomial.degree_eq_natDegree hp0, Polynomial.degree_eq_natDegree hq0]
-            rw [← Nat.cast_add, add_tsub_cancel_of_le, hn]
-            · refine' le_trans (Polynomial.natDegree_le_of_degree_le hdq) (le_of_lt h)
+            · rw [Polynomial.degree_eq_natDegree hp0, Polynomial.degree_eq_natDegree hq0]
+              rw [← Nat.cast_add, add_tsub_cancel_of_le, hn]
+              · refine' le_trans (Polynomial.natDegree_le_of_degree_le hdq) (le_of_lt h)
             rw [Polynomial.leadingCoeff_X_pow, mul_one]
             exact mt Polynomial.leadingCoeff_eq_zero.1 hq0
           have h2 : p.leadingCoeff = (q * Polynomial.X ^ (k - q.natDegree)).leadingCoeff := by

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

@@ -282,7 +282,7 @@ theorem geom_sum_X_comp_X_add_one_eq_sum (n : ℕ) :
       (Finset.range n).sum fun i : ℕ => (n.choose (i + 1) : R[X]) * X ^ i := by
   ext i
   trans (n.choose (i + 1) : R); swap
-  · simp only [finset_sum_coeff, ← C_eq_nat_cast, coeff_C_mul_X_pow]
+  · simp only [finset_sum_coeff, ← C_eq_natCast, coeff_C_mul_X_pow]
     rw [Finset.sum_eq_single i, if_pos rfl]
     · simp (config := { contextual := true }) only [@eq_comm _ i, if_false, eq_self_iff_true,
         imp_true_iff]

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

@@ -273,7 +273,7 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} := by
 
 theorem coeff_mem_frange (p : R[X]) (n : ℕ) (h : p.coeff n ≠ 0) : p.coeff n ∈ p.frange := by
   classical
-  simp only [frange, exists_prop, mem_support_iff, (Finset.mem_image), Ne]
+  simp only [frange, exists_prop, mem_support_iff, Finset.mem_image, Ne]
   exact ⟨n, h, rfl⟩
 #align polynomial.coeff_mem_frange Polynomial.coeff_mem_frange
 

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

@@ -5,15 +5,15 @@ Authors: Kenny Lau
 -/
 import Mathlib.Algebra.CharP.ExpChar
 import Mathlib.Algebra.GeomSum
-import Mathlib.Data.MvPolynomial.CommRing
-import Mathlib.Data.MvPolynomial.Equiv
+import Mathlib.Algebra.MvPolynomial.CommRing
+import Mathlib.Algebra.MvPolynomial.Equiv
 import Mathlib.RingTheory.Polynomial.Content
 import Mathlib.RingTheory.UniqueFactorizationDomain
 
 #align_import ring_theory.polynomial.basic from "leanprover-community/mathlib"@"da420a8c6dd5bdfb85c4ced85c34388f633bc6ff"
 
 /-!
-# Ring-theoretic supplement of Data.Polynomial.
+# Ring-theoretic supplement of Algebra.Polynomial.
 
 ## Main results
 * `MvPolynomial.isDomain`:

@@ -273,7 +273,7 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} := by
 
 theorem coeff_mem_frange (p : R[X]) (n : ℕ) (h : p.coeff n ≠ 0) : p.coeff n ∈ p.frange := by
   classical
-  simp only [frange, exists_prop, mem_support_iff, (Finset.mem_image), Ne.def]
+  simp only [frange, exists_prop, mem_support_iff, (Finset.mem_image), Ne]
   exact ⟨n, h, rfl⟩
 #align polynomial.coeff_mem_frange Polynomial.coeff_mem_frange
 
@@ -307,7 +307,7 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
     simp only [Nat.cast_lt, hP.natDegree_pow]
     intro k
     exact nsmul_lt_nsmul_left hdeg
-  · rw [bot_lt_iff_ne_bot, Ne.def, degree_eq_bot]
+  · rw [bot_lt_iff_ne_bot, Ne, degree_eq_bot]
     exact (hP.pow _).ne_zero
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
 
@@ -345,7 +345,7 @@ def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R))
 theorem coeff_restriction {p : R[X]} {n : ℕ} : ↑(coeff (restriction p) n) = coeff p n := by
   classical
   simp only [restriction, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
-    Ne.def, ite_not]
+    Ne, ite_not]
   split_ifs with h
   · rw [h]
     rfl
@@ -360,7 +360,7 @@ theorem coeff_restriction' {p : R[X]} {n : ℕ} : (coeff (restriction p) n).1 =
 @[simp]
 theorem support_restriction (p : R[X]) : support (restriction p) = support p := by
   ext i
-  simp only [mem_support_iff, not_iff_not, Ne.def]
+  simp only [mem_support_iff, not_iff_not, Ne]
   conv_rhs => rw [← coeff_restriction]
   exact ⟨fun H => by rw [H, ZeroMemClass.coe_zero], fun H => Subtype.coe_injective H⟩
 #align polynomial.support_restriction Polynomial.support_restriction
@@ -426,7 +426,7 @@ variable (hp : (↑p.frange : Set R) ⊆ T)
 theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n := by
   classical
   simp only [toSubring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
-    Ne.def, ite_not]
+    Ne, ite_not]
   split_ifs with h
   · rw [h]
     rfl
@@ -441,7 +441,7 @@ theorem coeff_toSubring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n
 @[simp]
 theorem support_toSubring : support (toSubring p T hp) = support p := by
   ext i
-  simp only [mem_support_iff, not_iff_not, Ne.def]
+  simp only [mem_support_iff, not_iff_not, Ne]
   conv_rhs => rw [← coeff_toSubring p T hp]
   exact ⟨fun H => by rw [H, ZeroMemClass.coe_zero], fun H => Subtype.coe_injective H⟩
 #align polynomial.support_to_subring Polynomial.support_toSubring
@@ -494,7 +494,7 @@ def ofSubring (p : T[X]) : R[X] :=
 
 theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff p n : T) := by
   simp only [ofSubring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
-    ite_eq_right_iff, Ne.def, ite_not, Classical.not_not, ite_eq_left_iff]
+    ite_eq_right_iff, Ne, ite_not, Classical.not_not, ite_eq_left_iff]
   intro h
   rw [h, ZeroMemClass.coe_zero]
 #align polynomial.coeff_of_subring Polynomial.coeff_ofSubring
@@ -503,7 +503,7 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T := by
   classical
   intro i hi
-  simp only [frange, Set.mem_image, mem_support_iff, Ne.def, Finset.mem_coe,
+  simp only [frange, Set.mem_image, mem_support_iff, Ne, Finset.mem_coe,
     (Finset.coe_image)] at hi
   rcases hi with ⟨n, _, h'n⟩
   rw [← h'n, coeff_ofSubring]
@@ -758,7 +758,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
       simpa only [coeff_C_zero] using h 0
   · intro h
     constructor
-    · rw [Ne.def, eq_top_iff_one, mem_map_C_iff, not_forall]
+    · rw [Ne, eq_top_iff_one, mem_map_C_iff, not_forall]
       use 0
       rw [coeff_one_zero, ← eq_top_iff_one]
       exact h.1
@@ -778,7 +778,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
         apply P.sum_mem
         rintro ⟨i, j⟩ hij
         rw [Finset.mem_erase, Finset.mem_antidiagonal] at hij
-        simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij
+        simp only [Ne, Prod.mk.inj_iff, not_and_or] at hij
         obtain hi | hj : i < m ∨ j < n := by
           rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
           rintro (hmi | rfl)

Cherry-picked from #9607 Co-authored-by: @semorrison

@@ -1211,10 +1211,10 @@ theorem map_mvPolynomial_eq_eval₂ {S : Type*} [CommRing S] [Finite σ] (ϕ : M
     ϕ p = MvPolynomial.eval₂ (ϕ.comp MvPolynomial.C) (fun s => ϕ (MvPolynomial.X s)) p := by
   cases nonempty_fintype σ
   refine' Trans.trans (congr_arg ϕ (MvPolynomial.as_sum p)) _
-  rw [MvPolynomial.eval₂_eq', ϕ.map_sum]
+  rw [MvPolynomial.eval₂_eq', map_sum ϕ]
   congr
   ext
-  simp only [monomial_eq, ϕ.map_pow, ϕ.map_prod, ϕ.comp_apply, ϕ.map_mul, Finsupp.prod_pow]
+  simp only [monomial_eq, ϕ.map_pow, map_prod ϕ, ϕ.comp_apply, ϕ.map_mul, Finsupp.prod_pow]
 #align mv_polynomial.map_mv_polynomial_eq_eval₂ MvPolynomial.map_mvPolynomial_eq_eval₂
 
 /-- If every coefficient of a polynomial is in an ideal `I`, then so is the polynomial itself,

Adds simp lemma for (p * q) %ₘ q = 0 and (q * p) %ₘ q = 0.

Also corrects a misspelling: dvd_iff_modByMonic_eq_zero should be modByMonic_eq_zero_iff_dvd

@@ -522,7 +522,7 @@ variable {q : R[X]}
 
 theorem mem_ker_modByMonic (hq : q.Monic) {p : R[X]} :
     p ∈ LinearMap.ker (modByMonicHom q) ↔ q ∣ p :=
-  LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
+  LinearMap.mem_ker.trans (modByMonic_eq_zero_iff_dvd hq)
 #align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_modByMonic
 
 @[simp]

@@ -197,7 +197,7 @@ theorem exists_degree_le_of_mem_span {s : Set R[X]} {p : R[X]}
   by_contra! h
   by_cases hp_zero : p = 0
   · rw [hp_zero, degree_zero] at h
-    rcases hs with ⟨x,hx⟩
+    rcases hs with ⟨x, hx⟩
     exact not_lt_bot (h x hx)
   · have : p ∈ degreeLT R (natDegree p) := by
       refine (Submodule.span_le.mpr fun p' p'_mem => ?_) hp
@@ -214,9 +214,8 @@ theorem exists_degree_le_of_mem_span_of_finite {s : Set R[X]} (s_fin : s.Finite)
   rcases Set.Finite.exists_maximal_wrt degree s s_fin hs with ⟨a, has, hmax⟩
   refine ⟨a, has, fun p hp => ?_⟩
   rcases exists_degree_le_of_mem_span hs hp with ⟨p', hp'⟩
-  have p'max := hmax p' hp'.left
   by_cases h : degree a ≤ degree p'
-  · rw [← p'max h] at hp'; exact hp'.right
+  · rw [← hmax p' hp'.left h] at hp'; exact hp'.right
   · exact le_trans hp'.right (not_le.mp h).le
 
 /-- The span of every finite set of polynomials is contained in a `degreeLE n` for some `n`. -/

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -815,7 +815,6 @@ end CommRing
 end Ideal
 
 variable {σ : Type v} {M : Type w}
-
 variable [CommRing R] [CommRing S] [AddCommGroup M] [Module R M]
 
 section Prime

This takes it from over 4 seconds to under 1 second on my machine. Most of the time was taken by erw and convert.

@@ -884,18 +884,23 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     have : (rename (↑)).toRingHom = eqv.toAlgHom.toRingHom.comp C := by
       apply ringHom_ext
       · intro
-        dsimp [eqv]
-        erw [iterToSum_C_C, rename_C, rename_C]
+        simp only [eqv, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, rename_C,
+          AlgEquiv.toAlgHom_eq_coe, AlgEquiv.toAlgHom_toRingHom, RingHom.coe_comp,
+          AlgEquiv.coe_trans, Function.comp_apply, MvPolynomial.sumAlgEquiv_symm_apply,
+          iterToSum_C_C, renameEquiv_apply, Equiv.coe_trans, Equiv.sumComm_apply]
       · intro
-        dsimp [eqv]
-        erw [iterToSum_C_X, rename_X, rename_X]
-        rfl
-    rw [← @prime_C_iff (MvPolynomial s R) (↥sᶜ) instCommRingMvPolynomial p]
-    rw [@MulEquiv.prime_iff (MvPolynomial ↑sᶜ (MvPolynomial ↑s R)) (MvPolynomial σ R) (_) (_)]
-    rotate_left
-    exact eqv.toMulEquiv
-    convert Iff.rfl
-    apply RingHom.congr_fun this p
+        simp only [eqv, AlgHom.toRingHom_eq_coe, RingHom.coe_coe, rename_X,
+          AlgEquiv.toAlgHom_eq_coe, AlgEquiv.toAlgHom_toRingHom, RingHom.coe_comp,
+          AlgEquiv.coe_trans, Function.comp_apply, MvPolynomial.sumAlgEquiv_symm_apply,
+          iterToSum_C_X, renameEquiv_apply, Equiv.coe_trans, Equiv.sumComm_apply, Sum.swap_inr,
+          Equiv.Set.sumCompl_apply_inl]
+    apply_fun (· p) at this
+    simp_rw [AlgHom.toRingHom_eq_coe, RingHom.coe_coe] at this
+    rw [← prime_C_iff, eqv.toMulEquiv.prime_iff, this]
+    simp only [MulEquiv.coe_mk, AlgEquiv.toEquiv_eq_coe, EquivLike.coe_coe, AlgEquiv.trans_apply,
+      MvPolynomial.sumAlgEquiv_symm_apply, renameEquiv_apply, Equiv.coe_trans, Equiv.sumComm_apply,
+      AlgEquiv.toAlgHom_eq_coe, AlgEquiv.toAlgHom_toRingHom, RingHom.coe_comp, RingHom.coe_coe,
+      AlgEquiv.coe_trans, Function.comp_apply]
 #align mv_polynomial.prime_rename_iff MvPolynomial.prime_rename_iff
 
 end MvPolynomial

Lean is so much more ergonomic now.

@@ -742,7 +742,7 @@ variable [CommRing R]
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) ↔ IsPrime P := by
-  -- Porting note: the following proof avoids quotient rings
+  -- Note: the following proof avoids quotient rings
   -- It can be golfed substantially by using something like
   -- `(Quotient.isDomain_iff_prime (map C P : Ideal R[X]))`
   constructor
@@ -807,8 +807,7 @@ theorem is_fg_degreeLE [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
     Submodule.FG (I.degreeLE n) :=
   letI := Classical.decEq R
   isNoetherian_submodule_left.1
-    -- porting note: times out without explicit `R`.
-    (isNoetherian_of_fg_of_noetherian _ ⟨_, (degreeLE_eq_span_X_pow (R := R)).symm⟩) _
+    (isNoetherian_of_fg_of_noetherian _ ⟨_, degreeLE_eq_span_X_pow.symm⟩) _
 #align ideal.is_fg_degree_le Ideal.is_fg_degreeLE
 
 end CommRing
@@ -825,10 +824,8 @@ variable (σ) {r : R}
 
 namespace Polynomial
 
--- Porting note: this ordering of the argument dramatically speeds up lean
 theorem prime_C_iff : Prime (C r) ↔ Prime r :=
-  ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, by
-    intro hr
+  ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, fun hr => by
     have := hr.1
     rw [← Ideal.span_singleton_prime] at hr ⊢
     · rw [← Set.image_singleton, ← Ideal.map_span]
@@ -842,15 +839,8 @@ end Polynomial
 
 namespace MvPolynomial
 
-/- Porting note: had to move the heavy inference outside the convert call to stop timeouts.
-Also, many @'s. etaExperiment caused more time outs-/
 private theorem prime_C_iff_of_fintype {R : Type u} (σ : Type v) {r : R} [CommRing R] [Fintype σ] :
     Prime (C r : MvPolynomial σ R) ↔ Prime r := by
-  let f (d : ℕ) := (finSuccEquiv R d).symm.toMulEquiv
-  let _coe' (d : ℕ) : CoeFun ((MvPolynomial (Fin d) R)[X] ≃* MvPolynomial (Fin (d + 1)) R)
-    (fun _ => (MvPolynomial (Fin d) R)[X] → MvPolynomial (Fin (d + 1)) R) := inferInstance
-  have that (d : ℕ) : @C R (Fin (d+1)) _ r = (f d) (Polynomial.C (@C R (Fin d) _ r)) := by
-    rw [← finSuccEquiv_comp_C_eq_C]; rfl
   rw [(renameEquiv R (Fintype.equivFin σ)).toMulEquiv.prime_iff]
   convert_to Prime (C r) ↔ _
   · congr!
@@ -859,16 +849,12 @@ private theorem prime_C_iff_of_fintype {R : Type u} (σ : Type v) {r : R} [CommR
     induction' Fintype.card σ with d hd
     · exact (isEmptyAlgEquiv R (Fin 0)).toMulEquiv.symm.prime_iff
     · rw [hd, ← Polynomial.prime_C_iff]
-      rw [that d]
-      -- Porting note: change ?_ to _ and watch it time out
-      refine @MulEquiv.prime_iff (MvPolynomial (Fin d) R)[X] (MvPolynomial (Fin (d + 1)) R)
-        ?_ ?_ (Polynomial.C (C r)) ?_
+      convert (finSuccEquiv R d).toMulEquiv.symm.prime_iff (p := Polynomial.C (C r))
+      rw [← finSuccEquiv_comp_C_eq_C]; rfl
 
--- Porting note: @'s help with multiple timeouts. It seems like there are too many things to unify
 theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
   ⟨comap_prime C constantCoeff (constantCoeff_C _), fun hr =>
-    ⟨fun h =>
-      hr.1 <| by
+    ⟨fun h => hr.1 <| by
         rw [← C_inj, h]
         simp,
       fun h =>
@@ -878,11 +864,10 @@ theorem prime_C_iff : Prime (C r : MvPolynomial σ R) ↔ Prime r :=
       fun a b hd => by
       obtain ⟨s, a', b', rfl, rfl⟩ := exists_finset_rename₂ a b
       rw [← algebraMap_eq] at hd
-      have := (@killCompl s σ R _ ((↑) : s → σ) Subtype.coe_injective).toRingHom.map_dvd hd
-      have : algebraMap R _ r ∣ a' * b' := by convert this <;> simp
+      have : algebraMap R _ r ∣ a' * b' := by
+        convert killCompl Subtype.coe_injective |>.toRingHom.map_dvd hd <;> simp
       rw [← rename_C ((↑) : s → σ)]
-      let f := @AlgHom.toRingHom R (MvPolynomial s R)
-        (MvPolynomial σ R) _ _ _ _ _ (@rename _ _ R _ ((↑) : s → σ))
+      let f := (rename (R := R) ((↑) : s → σ)).toRingHom
       exact (((prime_C_iff_of_fintype s).2 hr).2.2 a' b' this).imp f.map_dvd f.map_dvd⟩⟩
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.prime_C_iff MvPolynomial.prime_C_iff
@@ -1294,7 +1279,6 @@ open UniqueFactorizationMonoid
 
 namespace Polynomial
 
-attribute [-instance] Ring.toSemiring in
 instance (priority := 100) uniqueFactorizationMonoid : UniqueFactorizationMonoid D[X] := by
   letI := Classical.arbitrary (NormalizedGCDMonoid D)
   exact ufm_of_decomposition_of_wfDvdMonoid
@@ -1321,27 +1305,14 @@ end Polynomial
 namespace MvPolynomial
 variable (d : ℕ)
 
-/- Porting note: lean can come up with this instance in infinite time by resolving
-the diamond with CommSemiring.toSemiring. I don't know how to inline this
-attribute for a haveI in the proof of the uniqueFactorizationMonoid_of_fintype.
-The proof times out if we remove these from instance graph for all of
-uniqueFactorizationMonoid_of_fintype. -/
-attribute [-instance] Polynomial.semiring Polynomial.commSemiring in
-private instance : CancelCommMonoidWithZero (MvPolynomial (Fin d) D)[X] := by
-  apply IsDomain.toCancelCommMonoidWithZero
-
-/- Porting note: this can probably be cleaned up a little -/
 private theorem uniqueFactorizationMonoid_of_fintype [Fintype σ] :
     UniqueFactorizationMonoid (MvPolynomial σ D) :=
   (renameEquiv D (Fintype.equivFin σ)).toMulEquiv.symm.uniqueFactorizationMonoid <| by
     induction' Fintype.card σ with d hd
     · apply (isEmptyAlgEquiv D (Fin 0)).toMulEquiv.symm.uniqueFactorizationMonoid
       infer_instance
-    · rw [Nat.succ_eq_add_one d]
-      apply @MulEquiv.uniqueFactorizationMonoid _ _ (_) (_)
-      · exact (finSuccEquiv D d).toMulEquiv.symm
-      · apply @Polynomial.uniqueFactorizationMonoid (MvPolynomial (Fin d) D) _ _ ?_
-        assumption
+    · apply (finSuccEquiv D d).toMulEquiv.symm.uniqueFactorizationMonoid
+      exact Polynomial.uniqueFactorizationMonoid
 
 instance (priority := 100) uniqueFactorizationMonoid :
     UniqueFactorizationMonoid (MvPolynomial σ D) := by

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -899,10 +899,10 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     have : (rename (↑)).toRingHom = eqv.toAlgHom.toRingHom.comp C := by
       apply ringHom_ext
       · intro
-        dsimp
+        dsimp [eqv]
         erw [iterToSum_C_C, rename_C, rename_C]
       · intro
-        dsimp
+        dsimp [eqv]
         erw [iterToSum_C_X, rename_X, rename_X]
         rfl
     rw [← @prime_C_iff (MvPolynomial s R) (↥sᶜ) instCommRingMvPolynomial p]

This lemma is used in the proof of existence of Cartan subalgebras

@@ -1126,6 +1126,27 @@ end Polynomial
 
 namespace MvPolynomial
 
+lemma aeval_natDegree_le {R : Type*} [CommSemiring R] {m n : ℕ}
+    (F : MvPolynomial σ R) (hF : F.totalDegree ≤ m)
+    (f : σ → Polynomial R) (hf : ∀ i, (f i).natDegree ≤ n) :
+    (MvPolynomial.aeval f F).natDegree ≤ m * n := by
+  rw [MvPolynomial.aeval_def, MvPolynomial.eval₂]
+  apply (Polynomial.natDegree_sum_le _ _).trans
+  apply Finset.sup_le
+  intro d hd
+  simp_rw [Function.comp_apply, ← C_eq_algebraMap]
+  apply (Polynomial.natDegree_C_mul_le _ _).trans
+  apply (Polynomial.natDegree_prod_le _ _).trans
+  have : ∑ i in d.support, (d i) * n ≤ m * n := by
+    rw [← Finset.sum_mul]
+    apply mul_le_mul' (.trans _ hF) le_rfl
+    rw [MvPolynomial.totalDegree]
+    exact Finset.le_sup_of_le hd le_rfl
+  apply (Finset.sum_le_sum _).trans this
+  rintro i -
+  apply Polynomial.natDegree_pow_le.trans
+  exact mul_le_mul' le_rfl (hf i)
+
 theorem isNoetherianRing_fin_0 [IsNoetherianRing R] :
     IsNoetherianRing (MvPolynomial (Fin 0) R) := by
   apply isNoetherianRing_of_ringEquiv R

• Polynomial.map_contract: Polynomial.map and Polynomial.contract commutes
• Irreducible.natDegree_pos: an irreducible polynomial over a field must have positive degree (not true if it's not a field)
• Polynomial.Monic.nextCoeff_pow: corollary of Polynomial.Monic.nextCoeff_mul
• Polynomial.exists_monic_irreducible_factor: a polynomial over a field which is not a unit must have a monic irreducible factor (not true if it's not a field)

@@ -1339,3 +1339,14 @@ instance (priority := 100) uniqueFactorizationMonoid :
 end MvPolynomial
 
 end UniqueFactorizationDomain
+
+/-- A polynomial over a field which is not a unit must have a monic irreducible factor.
+See also `WfDvdMonoid.exists_irreducible_factor`. -/
+theorem Polynomial.exists_monic_irreducible_factor {F : Type*} [Field F] (f : F[X])
+    (hu : ¬IsUnit f) : ∃ g : F[X], g.Monic ∧ Irreducible g ∧ g ∣ f := by
+  by_cases hf : f = 0
+  · exact ⟨X, monic_X, irreducible_X, hf ▸ dvd_zero X⟩
+  obtain ⟨g, hi, hf⟩ := WfDvdMonoid.exists_irreducible_factor hu hf
+  have ha : Associated g (g * C g.leadingCoeff⁻¹) := associated_mul_unit_right _ _ <|
+    isUnit_C.2 (leadingCoeff_ne_zero.2 hi.ne_zero).isUnit.inv
+  exact ⟨_, monic_mul_leadingCoeff_inv hi.ne_zero, ha.irreducible hi, ha.dvd_iff_dvd_left.1 hf⟩

• Introduce typeclass DecompositionMonoid, which says every element in the monoid is primal, i.e., whenever an element divides a product b * c, it can be factored into a product such that the factors divides b and c respectively. A domain is called pre-Schreier if its multiplicative monoid is a decomposition monoid, and these are more general than GCD domains.

• Show that any GCDMonoid is a DecompositionMonoid. In order for lemmas about DecompositionMonoids to automatically apply to UniqueFactorizationMonoids, we add instances from UniqueFactorizationMonoid α to Nonempty (NormalizedGCDMonoid α) to Nonempty (GCDMonoid α) to DecompositionMonoid α. (Zulip) See the bottom of message for an updated diagram of classes and instances.

• Introduce binary predicate IsRelPrime which says that the only common divisors of the two elements are units. Replace previous occurrences in mathlib by this predicate.

• Duplicate all lemmas about IsCoprime in Coprime/Basic (except three lemmas about smul) to IsRelPrime. Due to import constraints, they are spread into three files Algebra/Divisibility/Units (including key lemmas assuming DecompositionMonoid), GroupWithZero/Divisibility, and Coprime/Basic.

• Show IsCoprime always imply IsRelPrime and is equivalent to it in Bezout rings. To reduce duplication, the definition of Bezout rings and the GCDMonoid instance are moved from RingTheory/Bezout to RingTheory/PrincipalIdealDomain, and some results in PrincipalIdealDomain are generalized to Bezout rings.

• Remove the recently added file Squarefree/UniqueFactorizationMonoid and place the results appropriately within Squarefree/Basic. All results are generalized to DecompositionMonoid or weaker except the last one.

Zulip

With this PR, all the following instances (indicated by arrows) now work; this PR fills the central part.

                                                                          EuclideanDomain (bundled)
                                                                              ↙          ↖
                                                                 IsPrincipalIdealRing ← Field (bundled)
                                                                            ↓             ↓
         NormalizationMonoid ←          NormalizedGCDMonoid → GCDMonoid  IsBezout ← ValuationRing ← DiscreteValuationRing
                   ↓                             ↓                 ↘       ↙
Nonempty NormalizationMonoid ← Nonempty NormalizedGCDMonoid →  Nonempty GCDMonoid → IsIntegrallyClosed
                                                 ↑                    ↓
                    WfDvdMonoid ← UniqueFactorizationMonoid → DecompositionMonoid
                                                 ↑
                                       IsPrincipalIdealRing

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -1275,11 +1275,8 @@ namespace Polynomial
 
 attribute [-instance] Ring.toSemiring in
 instance (priority := 100) uniqueFactorizationMonoid : UniqueFactorizationMonoid D[X] := by
-  letI := Classical.decEq (Associates D)
-  letI := Classical.decEq D
-  haveI : NormalizationMonoid D := Inhabited.default
-  haveI := toNormalizedGCDMonoid D
-  exact ufm_of_gcd_of_wfDvdMonoid
+  letI := Classical.arbitrary (NormalizedGCDMonoid D)
+  exact ufm_of_decomposition_of_wfDvdMonoid
 #align polynomial.unique_factorization_monoid Polynomial.uniqueFactorizationMonoid
 
 /-- If `D` is a unique factorization domain, `f` is a non-zero polynomial in `D[X]`, then `f` has

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -747,7 +747,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
   -- `(Quotient.isDomain_iff_prime (map C P : Ideal R[X]))`
   constructor
   · intro H
-    have := @comap_isPrime R R[X] (R →+* R[X]) _ _ _ C (map C P) H
+    have := comap_isPrime C (map C P)
     convert this using 1
     ext x
     simp only [mem_comap, mem_map_C_iff]

Consequently, the part about frobenius in Algebra/CharP/Basic is moved to CharP/ExpChar, and imports are adjusted as necessary.

• Add instances from CharP+Fact(Nat.Prime) and CharZero to ExpChar, to allow lemmas generalized to ExpChar still apply to CharP.

• Remove lemmas in Algebra/CharP/ExpChar from [#9799](https://github.com/leanprover-community/mathlib4/commit/1e74fcfff8d5ffe5a3a9881864cf10fa39f619e6) because they coincide with the generalized lemmas, and golf the other lemmas (in Algebra/CharP/Basic).

• Define the RingHom iterateFrobenius and the semilinear map LinearMap.(iterate)Frobenius for an algebra. When the characteristic is zero (ExpChar is 1), these are all equal to the identity map (· ^ 1). Also define iterateFrobeniusEquiv for perfect rings.

• Fix and/or generalize other files.

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

@@ -3,7 +3,7 @@ Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathlib.Algebra.CharP.Basic
+import Mathlib.Algebra.CharP.ExpChar
 import Mathlib.Algebra.GeomSum
 import Mathlib.Data.MvPolynomial.CommRing
 import Mathlib.Data.MvPolynomial.Equiv
@@ -47,6 +47,9 @@ instance instCharP (p : ℕ) [h : CharP R p] : CharP R[X] p :=
   let ⟨h⟩ := h
   ⟨fun n => by rw [← map_natCast C, ← C_0, C_inj, h]⟩
 
+instance instExpChar (p : ℕ) [h : ExpChar R p] : ExpChar R[X] p := by
+  cases h; exacts [ExpChar.zero, ExpChar.prime ‹_›]
+
 variable (R)
 
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree ≤ `n`. -/

@@ -1175,22 +1175,15 @@ theorem noZeroDivisors_of_finite (R : Type u) (σ : Type v) [CommSemiring R] [Fi
 #align mv_polynomial.no_zero_divisors_of_finite MvPolynomial.noZeroDivisors_of_finite
 
 instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
-    NoZeroDivisors (MvPolynomial σ R) :=
-  ⟨fun {p} {q} h => by
-    classical
-    obtain ⟨s, p, rfl⟩ := exists_finset_rename p
-    obtain ⟨t, q, rfl⟩ := exists_finset_rename q
-    have :
-        rename (Subtype.map id (Finset.subset_union_left s t) :
-          { x // x ∈ s } → { x // x ∈ s ∪ t }) p *
-        rename (Subtype.map id (Finset.subset_union_right s t) :
-          { x // x ∈ t } → { x // x ∈ s ∪ t }) q =
-        0 := by
+    NoZeroDivisors (MvPolynomial σ R) where
+  eq_zero_or_eq_zero_of_mul_eq_zero {p q} h := by
+    obtain ⟨s, p, q, rfl, rfl⟩ := exists_finset_rename₂ p q
+    let _nzd := MvPolynomial.noZeroDivisors_of_finite R s
+    have : p * q = 0 := by
       apply rename_injective _ Subtype.val_injective
       simpa using h
-    letI that := MvPolynomial.noZeroDivisors_of_finite R { x // x ∈ s ∪ t }
     rw [mul_eq_zero] at this
-    apply this.imp <;> intro that <;> simpa using congr_arg (rename Subtype.val) that⟩
+    apply this.imp <;> rintro rfl <;> simp
 
 /-- The multivariate polynomial ring over an integral domain is an integral domain. -/
 instance isDomain {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] :

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -9,7 +9,6 @@ import Mathlib.Data.MvPolynomial.CommRing
 import Mathlib.Data.MvPolynomial.Equiv
 import Mathlib.RingTheory.Polynomial.Content
 import Mathlib.RingTheory.UniqueFactorizationDomain
-import Mathlib.RingTheory.Ideal.QuotientOperations
 
 #align_import ring_theory.polynomial.basic from "leanprover-community/mathlib"@"da420a8c6dd5bdfb85c4ced85c34388f633bc6ff"
 

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -636,7 +636,7 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
     mem_degreeLE]
   constructor
   · rintro ⟨p, ⟨hpdeg, hpI⟩, rfl⟩
-    cases' lt_or_eq_of_le hpdeg with hpdeg hpdeg
+    rcases lt_or_eq_of_le hpdeg with hpdeg | hpdeg
     · refine' ⟨0, I.zero_mem, bot_le, _⟩
       rw [leadingCoeff_zero, eq_comm]
       exact coeff_eq_zero_of_degree_lt hpdeg
@@ -979,7 +979,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
         intro p hp
         generalize hn : p.natDegree = k
         induction' k using Nat.strong_induction_on with k ih generalizing p
-        cases' le_or_lt k N with h h
+        rcases le_or_lt k N with h | h
         · subst k
           refine' hs2 ⟨Polynomial.mem_degreeLE.2
             (le_trans Polynomial.degree_le_natDegree <| WithBot.coe_le_coe.2 h), hp⟩

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -305,7 +305,7 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
   · simp only [Finset.mem_range, degree_eq_natDegree (hP.pow _).ne_zero]
     simp only [Nat.cast_lt, hP.natDegree_pow]
     intro k
-    exact nsmul_lt_nsmul hdeg
+    exact nsmul_lt_nsmul_left hdeg
   · rw [bot_lt_iff_ne_bot, Ne.def, degree_eq_bot]
     exact (hP.pow _).ne_zero
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
@@ -698,7 +698,7 @@ theorem _root_.Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type*} (s : Finset
       apply sum_mem
       rintro ⟨i, j⟩ e
       obtain rfl : i + j = k := mem_antidiagonal.mp e
-      apply Ideal.pow_le_pow add_tsub_add_le_tsub_add_tsub
+      apply Ideal.pow_le_pow_right add_tsub_add_le_tsub_add_tsub
       rw [pow_add]
       exact
         Ideal.mul_mem_mul (h _ (Finset.mem_insert.mpr <| Or.inl rfl) _)

This shows with minimal requirements on R, that the R-module R[X] is not finite, or if R is a field, that equivalently R[X] is infinite-dimensional. On the way, some theorems are proven on how the R-span of a set of polynomials in R[X] interacts with the degree of the elements, and that the span of finitely many polynomials is always contained in some Polynomial.degreeLE n and some Polynomial.degreeLT n.

@@ -180,6 +180,72 @@ theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n)
   exact (sum_fin _ (by simp_rw [zero_mul, forall_const]) (mem_degreeLT.mp hp)).symm
 #align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquiv
 
+theorem degreeLT_succ_eq_degreeLE {n : ℕ} : degreeLT R (n + 1) = degreeLE R n := by
+  ext x
+  by_cases x_zero : x = 0
+  · simp_rw [x_zero, Submodule.zero_mem]
+  · rw [mem_degreeLT, mem_degreeLE, ← natDegree_lt_iff_degree_lt (by rwa [ne_eq]),
+      ← natDegree_le_iff_degree_le, Nat.lt_succ]
+
+/-- For every polynomial `p` in the span of a set `s : Set R[X]`, there exists a polynomial of
+  `p' ∈ s` with higher degree. See also `Polynomial.exists_degree_le_of_mem_span_of_finite`. -/
+theorem exists_degree_le_of_mem_span {s : Set R[X]} {p : R[X]}
+    (hs : s.Nonempty) (hp : p ∈ Submodule.span R s) :
+    ∃ p' ∈ s, degree p ≤ degree p' := by
+  by_contra! h
+  by_cases hp_zero : p = 0
+  · rw [hp_zero, degree_zero] at h
+    rcases hs with ⟨x,hx⟩
+    exact not_lt_bot (h x hx)
+  · have : p ∈ degreeLT R (natDegree p) := by
+      refine (Submodule.span_le.mpr fun p' p'_mem => ?_) hp
+      rw [SetLike.mem_coe, mem_degreeLT, Nat.cast_withBot]
+      exact lt_of_lt_of_le (h p' p'_mem) degree_le_natDegree
+    rwa [mem_degreeLT, Nat.cast_withBot, degree_eq_natDegree hp_zero,
+      Nat.cast_withBot, lt_self_iff_false] at this
+
+/-- A stronger version of `Polynomial.exists_degree_le_of_mem_span` under the assumption that the
+  set `s : R[X]` is finite. There exists a polynomial `p' ∈ s` whose degree dominates the degree of
+  every element of `p ∈ span R s`-/
+theorem exists_degree_le_of_mem_span_of_finite {s : Set R[X]} (s_fin : s.Finite) (hs : s.Nonempty) :
+    ∃ p' ∈ s, ∀ (p : R[X]), p ∈ Submodule.span R s → degree p ≤ degree p' := by
+  rcases Set.Finite.exists_maximal_wrt degree s s_fin hs with ⟨a, has, hmax⟩
+  refine ⟨a, has, fun p hp => ?_⟩
+  rcases exists_degree_le_of_mem_span hs hp with ⟨p', hp'⟩
+  have p'max := hmax p' hp'.left
+  by_cases h : degree a ≤ degree p'
+  · rw [← p'max h] at hp'; exact hp'.right
+  · exact le_trans hp'.right (not_le.mp h).le
+
+/-- The span of every finite set of polynomials is contained in a `degreeLE n` for some `n`. -/
+theorem span_le_degreeLE_of_finite {s : Set R[X]} (s_fin : s.Finite) :
+    ∃ n : ℕ, Submodule.span R s ≤ degreeLE R n := by
+  by_cases s_emp : s.Nonempty
+  · rcases exists_degree_le_of_mem_span_of_finite s_fin s_emp with ⟨p', _, hp'max⟩
+    exact ⟨natDegree p', fun p hp => mem_degreeLE.mpr ((hp'max _ hp).trans degree_le_natDegree)⟩
+  · rw [Set.not_nonempty_iff_eq_empty] at s_emp
+    rw [s_emp, Submodule.span_empty]
+    exact ⟨0, bot_le⟩
+
+/-- The span of every finite set of polynomials is contained in a `degreeLT n` for some `n`. -/
+theorem span_of_finite_le_degreeLT {s : Set R[X]} (s_fin : s.Finite) :
+    ∃ n : ℕ, Submodule.span R s ≤ degreeLT R n := by
+  rcases span_le_degreeLE_of_finite s_fin with ⟨n, _⟩
+  exact ⟨n + 1, by rwa [degreeLT_succ_eq_degreeLE]⟩
+
+/-- If `R` is a nontrivial ring, the polynomials `R[X]` are not finite as an `R`-module. When `R` is
+a field, this is equivalent to `R[X]` being an infinite-dimensional vector space over `R`.  -/
+theorem not_finite [Nontrivial R] : ¬ Module.Finite R R[X] := by
+  rw [Module.finite_def, Submodule.fg_def]
+  push_neg
+  intro s hs contra
+  rcases span_le_degreeLE_of_finite hs with ⟨n,hn⟩
+  have : ((X : R[X]) ^ (n + 1)) ∈ Polynomial.degreeLE R ↑n := by
+    rw [contra] at hn
+    exact hn Submodule.mem_top
+  rw [mem_degreeLE, degree_X_pow, Nat.cast_le, add_le_iff_nonpos_right, nonpos_iff_eq_zero] at this
+  exact one_ne_zero this
+
 /-- The finset of nonzero coefficients of a polynomial. -/
 def frange (p : R[X]) : Finset R :=
   letI := Classical.decEq R

Added Field.exists_primitive_element_iff_finite_intermediateField: a finite extension E / F has a primitive element if and only if the intermediate fields between E / F are finitely many. Also known as Steinitz Theorem https://en.wikipedia.org/wiki/Primitive_element_theorem#The_theorems.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Junyan Xu <junyanxumath@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -851,8 +851,8 @@ end Prime
 
 namespace Polynomial
 
-instance (priority := 100) {R : Type*} [CommRing R] [IsDomain R] [WfDvdMonoid R] : WfDvdMonoid R[X]
-    where
+instance (priority := 100) wfDvdMonoid {R : Type*} [CommRing R] [IsDomain R] [WfDvdMonoid R] :
+    WfDvdMonoid R[X] where
   wellFounded_dvdNotUnit := by
     classical
       refine'
@@ -1128,7 +1128,7 @@ instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
     apply this.imp <;> intro that <;> simpa using congr_arg (rename Subtype.val) that⟩
 
 /-- The multivariate polynomial ring over an integral domain is an integral domain. -/
-instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] :
+instance isDomain {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] :
     IsDomain (MvPolynomial σ R) := by
   apply @NoZeroDivisors.to_isDomain (MvPolynomial σ R) _ ?_ _
   apply AddMonoidAlgebra.nontrivial
@@ -1221,6 +1221,22 @@ instance (priority := 100) uniqueFactorizationMonoid : UniqueFactorizationMonoid
   exact ufm_of_gcd_of_wfDvdMonoid
 #align polynomial.unique_factorization_monoid Polynomial.uniqueFactorizationMonoid
 
+/-- If `D` is a unique factorization domain, `f` is a non-zero polynomial in `D[X]`, then `f` has
+only finitely many monic factors.
+(Note that its factors up to unit may be more than monic factors.)
+See also `UniqueFactorizationMonoid.fintypeSubtypeDvd`. -/
+noncomputable def fintypeSubtypeMonicDvd (f : D[X]) (hf : f ≠ 0) :
+    Fintype { g : D[X] // g.Monic ∧ g ∣ f } := by
+  set G := { g : D[X] // g.Monic ∧ g ∣ f }
+  let y : Associates D[X] := Associates.mk f
+  have hy : y ≠ 0 := Associates.mk_ne_zero.mpr hf
+  let H := { x : Associates D[X] // x ∣ y }
+  let hfin : Fintype H := UniqueFactorizationMonoid.fintypeSubtypeDvd y hy
+  let i : G → H := fun x ↦ ⟨Associates.mk x.1, Associates.mk_dvd_mk.2 x.2.2⟩
+  refine Fintype.ofInjective i fun x y heq ↦ ?_
+  rw [Subtype.mk.injEq] at heq ⊢
+  exact eq_of_monic_of_associated x.2.1 y.2.1 (Associates.mk_eq_mk_iff_associated.mp heq)
+
 end Polynomial
 
 namespace MvPolynomial
@@ -1248,7 +1264,8 @@ private theorem uniqueFactorizationMonoid_of_fintype [Fintype σ] :
       · apply @Polynomial.uniqueFactorizationMonoid (MvPolynomial (Fin d) D) _ _ ?_
         assumption
 
-instance (priority := 100) : UniqueFactorizationMonoid (MvPolynomial σ D) := by
+instance (priority := 100) uniqueFactorizationMonoid :
+    UniqueFactorizationMonoid (MvPolynomial σ D) := by
   rw [iff_exists_prime_factors]
   intro a ha; obtain ⟨s, a', rfl⟩ := exists_finset_rename a
   obtain ⟨w, h, u, hw⟩ :=

This PR defines the reduce_mod_char tactic, which traverses expressions looking for numerals n, such that the type of n is a ring of (positive) characteristic p, and reduces these numerals modulo p, to lie between 0 and p.

This is one of my first Lean 4 metaprogramming projects, so I eagerly await you pointing out all my mistakes. Especially I would like to learn where I should insert those magical withContext and instantiateMVars incantations.

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/tactic.20for.20easy.20calculations.20in.20ZMod.20p.3F

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -44,7 +44,7 @@ section Semiring
 
 variable [Semiring R]
 
-instance (p : ℕ) [h : CharP R p] : CharP R[X] p :=
+instance instCharP (p : ℕ) [h : CharP R p] : CharP R[X] p :=
   let ⟨h⟩ := h
   ⟨fun n => by rw [← map_natCast C, ← C_0, C_inj, h]⟩
 

We already have WellFoundedLT/WellFoundedGT as wrappers around IsWellFounded, but we didn't have the corresponding wrapper lemmas.

@@ -860,8 +860,7 @@ instance (priority := 100) {R : Type*} [CommRing R] [IsDomain R] [WfDvdMonoid R]
           (⟨fun p : R[X] =>
               ((if p = 0 then ⊤ else ↑p.degree : WithTop (WithBot ℕ)), p.leadingCoeff), _⟩ :
             DvdNotUnit →r Prod.Lex (· < ·) DvdNotUnit)
-          (WellFounded.prod_lex (WithTop.wellFounded_lt <| WithBot.wellFounded_lt Nat.lt_wfRel.wf)
-            ‹WfDvdMonoid R›.wellFounded_dvdNotUnit)
+          (wellFounded_lt.prod_lex ‹WfDvdMonoid R›.wellFounded_dvdNotUnit)
       rintro a b ⟨ane0, ⟨c, ⟨not_unit_c, rfl⟩⟩⟩
       dsimp
       rw [Polynomial.degree_mul, if_neg ane0]

We define a type class Finset.HasAntidiagonal A which contains a function antidiagonal : A → Finset (A × A) such that antidiagonal n is the Finset of all pairs adding to n, as witnessed by mem_antidiagonal.

When A is a canonically ordered add monoid with locally finite order this typeclass can be instantiated with Finset.antidiagonalOfLocallyFinite. This applies in particular when A is ℕ, more generally or σ →₀ ℕ, or even ι →₀ A under the additional assumption OrderedSub A that make it a canonically ordered add monoid. (In fact, we would just need an AddMonoid with a compatible order, finite Iic, such that if a + b = n, then a, b ≤ n, and any finiteness condition would be OK.)

For computational reasons it is better to manually provide instances for ℕ and σ →₀ ℕ, to avoid quadratic runtime performance. These instances are provided as Finset.Nat.instHasAntidiagonal and Finsupp.instHasAntidiagonal. This is why Finset.antidiagonalOfLocallyFinite is an abbrev and not an instance.

This definition does not exactly match with that of Multiset.antidiagonal defined in Mathlib.Data.Multiset.Antidiagonal, because of the multiplicities. Indeed, by counting multiplicities, Multiset α is equivalent to α →₀ ℕ, but Finset.antidiagonal and Multiset.antidiagonal will return different objects. For example, for s : Multiset ℕ := {0,0,0}, Multiset.antidiagonal s has 8 elements but Finset.antidiagonal s has only 4.

def s : Multiset ℕ := {0, 0, 0}
#eval (Finset.antidiagonal s).card -- 4
#eval Multiset.card (Multiset.antidiagonal s) -- 8

TODO

• Define HasMulAntidiagonal (for monoids). For PNat, we will recover the set of divisors of a strictly positive integer.

This closes #7917

Co-authored by: María Inés de Frutos-Fernández <mariaines.dff@gmail.com> and Eric Wieser <efw27@cam.ac.uk>

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -631,7 +631,7 @@ theorem _root_.Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type*} (s : Finset
     · rw [sum_insert ha, prod_insert ha, coeff_mul]
       apply sum_mem
       rintro ⟨i, j⟩ e
-      obtain rfl : i + j = k := Nat.mem_antidiagonal.mp e
+      obtain rfl : i + j = k := mem_antidiagonal.mp e
       apply Ideal.pow_le_pow add_tsub_add_le_tsub_add_tsub
       rw [pow_add]
       exact
@@ -703,14 +703,14 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
         let m := Nat.find hf
         let n := Nat.find hg
         refine' ⟨m + n, _⟩
-        rw [coeff_mul, ← Finset.insert_erase ((@Finset.Nat.mem_antidiagonal _ (m, n)).mpr rfl),
+        rw [coeff_mul, ← Finset.insert_erase ((Finset.mem_antidiagonal (a := (m,n))).mpr rfl),
           Finset.sum_insert (Finset.not_mem_erase _ _), (P.add_mem_iff_left _).not]
         · apply mt h.2
           rw [not_or]
           exact ⟨Nat.find_spec hf, Nat.find_spec hg⟩
         apply P.sum_mem
         rintro ⟨i, j⟩ hij
-        rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij
+        rw [Finset.mem_erase, Finset.mem_antidiagonal] at hij
         simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij
         obtain hi | hj : i < m ∨ j < n := by
           rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]

Removes nonterminal simps on lines looking like simp [...]

@@ -547,7 +547,7 @@ theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
   · intro hf
     rw [← sum_monomial_eq f]
     refine' (I.map C : Ideal R[X]).sum_mem fun n _ => _
-    simp [← C_mul_X_pow_eq_monomial]
+    simp only [← C_mul_X_pow_eq_monomial, ne_eq]
     rw [mul_comm]
     exact (I.map C : Ideal R[X]).mul_mem_left _ (mem_map_of_mem _ (hf n))
 set_option linter.uppercaseLean3 false in

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.

@@ -30,7 +30,7 @@ import Mathlib.RingTheory.Ideal.QuotientOperations
 
 noncomputable section
 
-open Classical BigOperators Polynomial
+open BigOperators Polynomial
 
 open Finset
 
@@ -71,7 +71,7 @@ theorem degreeLE_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLE R m ≤ degre
   mem_degreeLE.2 (le_trans (mem_degreeLE.1 hf) H)
 #align polynomial.degree_le_mono Polynomial.degreeLE_mono
 
-theorem degreeLE_eq_span_X_pow {n : ℕ} :
+theorem degreeLE_eq_span_X_pow [DecidableEq R] {n : ℕ} :
     degreeLE R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) := by
   apply le_antisymm
   · intro p hp
@@ -111,7 +111,7 @@ theorem degreeLT_mono {m n : ℕ} (H : m ≤ n) : degreeLT R m ≤ degreeLT R n
   mem_degreeLT.2 (lt_of_lt_of_le (mem_degreeLT.1 hf) <| WithBot.coe_le_coe.2 H)
 #align polynomial.degree_lt_mono Polynomial.degreeLT_mono
 
-theorem degreeLT_eq_span_X_pow {n : ℕ} :
+theorem degreeLT_eq_span_X_pow [DecidableEq R] {n : ℕ} :
     degreeLT R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) := by
   apply le_antisymm
   · intro p hp
@@ -182,6 +182,7 @@ theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n)
 
 /-- The finset of nonzero coefficients of a polynomial. -/
 def frange (p : R[X]) : Finset R :=
+  letI := Classical.decEq R
   Finset.image (fun n => p.coeff n) p.support
 #align polynomial.frange Polynomial.frange
 
@@ -190,10 +191,11 @@ theorem frange_zero : frange (0 : R[X]) = ∅ :=
 #align polynomial.frange_zero Polynomial.frange_zero
 
 theorem mem_frange_iff {p : R[X]} {c : R} : c ∈ p.frange ↔ ∃ n ∈ p.support, c = p.coeff n := by
-  simp [frange, eq_comm]
+  simp [frange, eq_comm, (Finset.mem_image)]
 #align polynomial.mem_frange_iff Polynomial.mem_frange_iff
 
 theorem frange_one : frange (1 : R[X]) ⊆ {1} := by
+  classical
   simp only [frange]
   rw [Finset.image_subset_iff]
   simp only [mem_support_iff, ne_eq, mem_singleton, ← C_1, coeff_C]
@@ -203,7 +205,8 @@ theorem frange_one : frange (1 : R[X]) ⊆ {1} := by
 #align polynomial.frange_one Polynomial.frange_one
 
 theorem coeff_mem_frange (p : R[X]) (n : ℕ) (h : p.coeff n ≠ 0) : p.coeff n ∈ p.frange := by
-  simp only [frange, exists_prop, mem_support_iff, Finset.mem_image, Ne.def]
+  classical
+  simp only [frange, exists_prop, mem_support_iff, (Finset.mem_image), Ne.def]
   exact ⟨n, h, rfl⟩
 #align polynomial.coeff_mem_frange Polynomial.coeff_mem_frange
 
@@ -265,6 +268,7 @@ def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R))
   ∑ i in p.support,
     monomial i
       (⟨p.coeff i,
+          letI := Classical.decEq R
           if H : p.coeff i = 0 then H.symm ▸ (Subring.closure _).zero_mem
           else Subring.subset_closure (p.coeff_mem_frange _ H)⟩ :
         Subring.closure (↑p.frange : Set R))
@@ -272,6 +276,7 @@ def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R))
 
 @[simp]
 theorem coeff_restriction {p : R[X]} {n : ℕ} : ↑(coeff (restriction p) n) = coeff p n := by
+  classical
   simp only [restriction, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
     Ne.def, ite_not]
   split_ifs with h
@@ -343,14 +348,16 @@ return the corresponding polynomial whose coefficients are in `T`. -/
 def toSubring (hp : (↑p.frange : Set R) ⊆ T) : T[X] :=
   ∑ i in p.support,
     monomial i
-      (⟨p.coeff i, if H : p.coeff i = 0 then H.symm ▸ T.zero_mem else hp (p.coeff_mem_frange _ H)⟩ :
-        T)
+      (⟨p.coeff i,
+        letI := Classical.decEq R
+        if H : p.coeff i = 0 then H.symm ▸ T.zero_mem else hp (p.coeff_mem_frange _ H)⟩ : T)
 #align polynomial.to_subring Polynomial.toSubring
 
 variable (hp : (↑p.frange : Set R) ⊆ T)
 
 @[simp]
 theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n := by
+  classical
   simp only [toSubring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
     Ne.def, ite_not]
   split_ifs with h
@@ -427,8 +434,10 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
 
 @[simp]
 theorem frange_ofSubring {p : T[X]} : (↑(p.ofSubring T).frange : Set R) ⊆ T := by
+  classical
   intro i hi
-  simp only [frange, Set.mem_image, mem_support_iff, Ne.def, Finset.mem_coe, Finset.coe_image] at hi
+  simp only [frange, Set.mem_image, mem_support_iff, Ne.def, Finset.mem_coe,
+    (Finset.coe_image)] at hi
   rcases hi with ⟨n, _, h'n⟩
   rw [← h'n, coeff_ofSubring]
   exact Subtype.mem (coeff p n : T)
@@ -728,6 +737,7 @@ set_option linter.uppercaseLean3 false in
 
 theorem is_fg_degreeLE [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
     Submodule.FG (I.degreeLE n) :=
+  letI := Classical.decEq R
   isNoetherian_submodule_left.1
     -- porting note: times out without explicit `R`.
     (isNoetherian_of_fg_of_noetherian _ ⟨_, (degreeLE_eq_span_X_pow (R := R)).symm⟩) _
@@ -1103,6 +1113,7 @@ theorem noZeroDivisors_of_finite (R : Type u) (σ : Type v) [CommSemiring R] [Fi
 instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
     NoZeroDivisors (MvPolynomial σ R) :=
   ⟨fun {p} {q} h => by
+    classical
     obtain ⟨s, p, rfl⟩ := exists_finset_rename p
     obtain ⟨t, q, rfl⟩ := exists_finset_rename q
     have :
@@ -1155,6 +1166,7 @@ theorem mem_ideal_of_coeff_mem_ideal (I : Ideal (MvPolynomial σ R)) (p : MvPoly
 theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
     f ∈ (Ideal.map (C : R →+* MvPolynomial σ R) I : Ideal (MvPolynomial σ R)) ↔
       ∀ m : σ →₀ ℕ, f.coeff m ∈ I := by
+  classical
   constructor
   · intro hf
     apply @Submodule.span_induction _ _ _ _ Semiring.toModule f _ _ hf
@@ -1203,6 +1215,8 @@ namespace Polynomial
 
 attribute [-instance] Ring.toSemiring in
 instance (priority := 100) uniqueFactorizationMonoid : UniqueFactorizationMonoid D[X] := by
+  letI := Classical.decEq (Associates D)
+  letI := Classical.decEq D
   haveI : NormalizationMonoid D := Inhabited.default
   haveI := toNormalizedGCDMonoid D
   exact ufm_of_gcd_of_wfDvdMonoid

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.

@@ -549,7 +549,8 @@ theorem _root_.Polynomial.ker_mapRingHom (f : R →+* S) :
   ext
   simp only [LinearMap.mem_ker, RingHom.toSemilinearMap_apply, coe_mapRingHom]
   rw [mem_map_C_iff, Polynomial.ext_iff]
-  simp_rw [RingHom.mem_ker f, coeff_map, coeff_zero]
+  simp_rw [RingHom.mem_ker f]
+  simp
 #align polynomial.ker_map_ring_hom Polynomial.ker_mapRingHom
 
 variable (I : Ideal R[X])

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

@@ -898,7 +898,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
       ⟨s, le_antisymm (Ideal.span_le.2 fun x hx =>
           have : x ∈ I.degreeLE N := hs ▸ Submodule.subset_span hx
           this.2) <| by
-        have : Submodule.span R[X] ↑s = Ideal.span ↑s := by rfl
+        have : Submodule.span R[X] ↑s = Ideal.span ↑s := rfl
         rw [this]
         intro p hp
         generalize hn : p.natDegree = k

Also WithBot.charZero

@@ -155,8 +155,7 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
     by_cases hp0 : p = 0
     · subst hp0
       simp only [coeff_zero, LinearMap.map_zero, Finset.sum_const_zero]
-    rw [mem_degreeLT, degree_eq_natDegree hp0,
-      Nat.cast_withBot, Nat.cast_withBot, WithBot.coe_lt_coe] at hp
+    rw [mem_degreeLT, degree_eq_natDegree hp0, Nat.cast_lt] at hp
     conv_rhs => rw [p.as_sum_range' n hp, ← Fin.sum_univ_eq_sum_range]
   right_inv f := by
     ext i
@@ -235,7 +234,7 @@ theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : 
   refine' lt_of_le_of_lt (degree_sum_le _ _) _
   rw [Finset.sup_lt_iff]
   · simp only [Finset.mem_range, degree_eq_natDegree (hP.pow _).ne_zero]
-    simp only [Nat.cast_withBot, WithBot.coe_lt_coe, hP.natDegree_pow]
+    simp only [Nat.cast_lt, hP.natDegree_pow]
     intro k
     exact nsmul_lt_nsmul hdeg
   · rw [bot_lt_iff_ne_bot, Ne.def, degree_eq_bot]
@@ -573,7 +572,7 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
     refine' ⟨p * X ^ (n - natDegree p), ⟨_, I.mul_mem_right _ hpI⟩, _⟩
     · apply le_trans (degree_mul_le _ _) _
       apply le_trans (add_le_add degree_le_natDegree (degree_X_pow_le _)) _
-      rw [Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add, this, Nat.cast_withBot]
+      rw [← Nat.cast_add, this]
     · rw [Polynomial.leadingCoeff, ← coeff_mul_X_pow p (n - natDegree p), this]
 #align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNth
 
@@ -592,8 +591,7 @@ theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤
   refine' ⟨p * X ^ (n - m), I.mul_mem_right _ hpI, _, leadingCoeff_mul_X_pow⟩
   refine' le_trans (degree_mul_le _ _) _
   refine' le_trans (add_le_add hpdeg (degree_X_pow_le _)) _
-  rw [Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add, add_tsub_cancel_of_le H,
-    Nat.cast_withBot]
+  rw [← Nat.cast_add, add_tsub_cancel_of_le H]
 #align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_mono
 
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x := by
@@ -871,8 +869,7 @@ instance (priority := 100) {R : Type*} [CommRing R] [IsDomain R] [WfDvdMonoid R]
         rw [Polynomial.leadingCoeff, Polynomial.natDegree_eq_of_degree_eq_some hdeg]; rfl
       · apply Prod.Lex.left
         rw [Polynomial.degree_eq_natDegree cne0] at *
-        rw [WithTop.coe_lt_coe, Polynomial.degree_eq_natDegree ane0,
-          Nat.cast_withBot, Nat.cast_withBot,← WithBot.coe_add, WithBot.coe_lt_coe]
+        rw [WithTop.coe_lt_coe, Polynomial.degree_eq_natDegree ane0, ← Nat.cast_add, Nat.cast_lt]
         exact lt_add_of_pos_right _ (Nat.pos_of_ne_zero fun h => hdeg (h.symm ▸ WithBot.coe_zero))
 
 end Polynomial
@@ -936,8 +933,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
           have h1 : p.degree = (q * Polynomial.X ^ (k - q.natDegree)).degree := by
             rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
             rw [Polynomial.degree_eq_natDegree hp0, Polynomial.degree_eq_natDegree hq0]
-            rw [Nat.cast_withBot, Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add,
-              add_tsub_cancel_of_le, hn]
+            rw [← Nat.cast_add, add_tsub_cancel_of_le, hn]
             · refine' le_trans (Polynomial.natDegree_le_of_degree_le hdq) (le_of_lt h)
             rw [Polynomial.leadingCoeff_X_pow, mul_one]
             exact mt Polynomial.leadingCoeff_eq_zero.1 hq0
@@ -951,8 +947,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
             · rw [hpq]
               exact Ideal.zero_mem _
             refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
-            rwa [Polynomial.degree_eq_natDegree hpq, Nat.cast_withBot, Nat.cast_withBot,
-              WithBot.coe_lt_coe, hn] at this
+            rwa [Polynomial.degree_eq_natDegree hpq, Nat.cast_lt, hn] at this
           exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
 #align polynomial.is_noetherian_ring Polynomial.isNoetherianRing
 

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).

@@ -178,7 +178,7 @@ theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degre
 theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
     p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) := by
   simp_rw [eval_eq_sum]
-  exact (sum_fin _ (by simp_rw [MulZeroClass.zero_mul, forall_const]) (mem_degreeLT.mp hp)).symm
+  exact (sum_fin _ (by simp_rw [zero_mul, forall_const]) (mem_degreeLT.mp hp)).symm
 #align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquiv
 
 /-- The finset of nonzero coefficients of a polynomial. -/
@@ -919,7 +919,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
             apply hp0
             ext i
             refine' (mul_one _).symm.trans _
-            rw [← h, MulZeroClass.mul_zero]
+            rw [← h, mul_zero]
             rfl
           haveI : Nontrivial R := ⟨⟨0, 1, this⟩⟩
           have : p.leadingCoeff ∈ I.leadingCoeffNth N := by

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

@@ -221,7 +221,7 @@ theorem geom_sum_X_comp_X_add_one_eq_sum (n : ℕ) :
         Nat.cast_zero, Finset.mem_range, not_lt, eq_self_iff_true, if_true, imp_true_iff]
   induction' n with n ih generalizing i
   · dsimp; simp only [zero_comp, coeff_zero, Nat.cast_zero]
-  · dsimp; simp only [geom_sum_succ', ih, add_comp, X_pow_comp, coeff_add, Nat.choose_succ_succ,
+  · simp only [geom_sum_succ', ih, add_comp, X_pow_comp, coeff_add, Nat.choose_succ_succ,
     Nat.cast_add, coeff_X_add_one_pow]
 set_option linter.uppercaseLean3 false in
 #align polynomial.geom_sum_X_comp_X_add_one_eq_sum Polynomial.geom_sum_X_comp_X_add_one_eq_sum

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

This has nice performance benefits.

@@ -36,7 +36,7 @@ open Finset
 
 universe u v w
 
-variable {R : Type u} {S : Type _}
+variable {R : Type u} {S : Type*}
 
 namespace Polynomial
 
@@ -613,7 +613,7 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
 /-- If `I` is an ideal, and `pᵢ` is a finite family of polynomials each satisfying
 `∀ k, (pᵢ)ₖ ∈ Iⁿⁱ⁻ᵏ` for some `nᵢ`, then `p = ∏ pᵢ` also satisfies `∀ k, pₖ ∈ Iⁿ⁻ᵏ` with `n = ∑ nᵢ`.
 -/
-theorem _root_.Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type _} (s : Finset ι) (f : ι → R[X])
+theorem _root_.Polynomial.coeff_prod_mem_ideal_pow_tsub {ι : Type*} (s : Finset ι) (f : ι → R[X])
     (I : Ideal R) (n : ι → ℕ) (h : ∀ i ∈ s, ∀ (k), (f i).coeff k ∈ I ^ (n i - k)) (k : ℕ) :
     (s.prod f).coeff k ∈ I ^ (s.sum n - k) := by
   classical
@@ -842,7 +842,7 @@ end Prime
 
 namespace Polynomial
 
-instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R] : WfDvdMonoid R[X]
+instance (priority := 100) {R : Type*} [CommRing R] [IsDomain R] [WfDvdMonoid R] : WfDvdMonoid R[X]
     where
   wellFounded_dvdNotUnit := by
     classical
@@ -1130,7 +1130,7 @@ instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] :
 -- instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] :
 --     IsDomain (MvPolynomial σ R)[X] := inferInstance
 
-theorem map_mvPolynomial_eq_eval₂ {S : Type _} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
+theorem map_mvPolynomial_eq_eval₂ {S : Type*} [CommRing S] [Finite σ] (ϕ : MvPolynomial σ R →+* S)
     (p : MvPolynomial σ R) :
     ϕ p = MvPolynomial.eval₂ (ϕ.comp MvPolynomial.C) (fun s => ϕ (MvPolynomial.X s)) p := by
   cases nonempty_fintype σ

@@ -254,13 +254,6 @@ theorem monic_geom_sum_X {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (X : R[X]
 set_option linter.uppercaseLean3 false in
 #align polynomial.monic_geom_sum_X Polynomial.monic_geom_sum_X
 
-theorem IsNilpotent.C_mul_X_pow_isNilpotent {r : R} (n : ℕ) (hnil : IsNilpotent r) :
-    IsNilpotent ((C r) * X ^ n) := by
-  refine' Commute.isNilpotent_mul_left (commute_X_pow _ _).symm _
-  obtain ⟨m, hm⟩ := hnil
-  refine' ⟨m, _⟩
-  rw [← C_pow, hm, C_0]
-
 end Semiring
 
 section Ring
@@ -465,58 +458,6 @@ theorem ker_modByMonicHom (hq : q.Monic) :
 
 end ModByMonic
 
-/-- Let `P` be a polynomial over `R`. If its constant term is a unit and its other coefficients are
-nilpotent, then `P` is a unit. -/
-theorem isUnit_of_coeff_isUnit_isNilpotent {P : Polynomial R} (hunit : IsUnit (P.coeff 0))
-    (hnil : ∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) : IsUnit P := by
-  induction' h : P.natDegree using Nat.strong_induction_on with k hind generalizing P
-  by_cases hdeg : P.natDegree = 0
-  { rw [eq_C_of_natDegree_eq_zero hdeg]
-    exact hunit.map C }
-  set P₁ := P.eraseLead with hP₁
-  suffices IsUnit P₁ by
-    rw [← eraseLead_add_monomial_natDegree_leadingCoeff P, ← C_mul_X_pow_eq_monomial]
-    obtain ⟨Q, hQ⟩ := this
-    rw [← hP₁, ← hQ]
-    refine' Commute.IsNilpotent.add_isUnit (IsNilpotent.C_mul_X_pow_isNilpotent _ (hnil _ hdeg))
-      ((Commute.all _ _).mul_left (Commute.all _ _))
-  have hdeg₂ := lt_of_le_of_lt P.eraseLead_natDegree_le (Nat.sub_lt
-    (Nat.pos_of_ne_zero hdeg) zero_lt_one)
-  refine' hind P₁.natDegree _ _ (fun i hi => _) rfl
-  · simp_rw [← h, hdeg₂]
-  · simp_rw [eraseLead_coeff_of_ne _ (Ne.symm hdeg), hunit]
-  · by_cases H : i ≤ P₁.natDegree
-    simp_rw [eraseLead_coeff_of_ne _ (ne_of_lt (lt_of_le_of_lt H hdeg₂)), hnil i hi]
-    simp_rw [coeff_eq_zero_of_natDegree_lt (lt_of_not_ge H), IsNilpotent.zero]
-
-/-- Let `P` be a polynomial over `R`. If `P` is a unit, then all its coefficients are nilpotent,
-except its constant term which is a unit. -/
-theorem coeff_isUnit_isNilpotent_of_isUnit {P : Polynomial R} (hunit : IsUnit P) :
-    IsUnit (P.coeff 0) ∧ (∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) := by
-  obtain ⟨Q, hQ⟩ := IsUnit.exists_right_inv hunit
-  constructor
-  · refine' isUnit_of_mul_eq_one _ (Q.coeff 0) _
-    have h := (mul_coeff_zero P Q).symm
-    rwa [hQ, coeff_one_zero] at h
-  · intros n hn
-    rw [nilpotent_iff_mem_prime]
-    intros I hI
-    let f := mapRingHom (Ideal.Quotient.mk I)
-    have hPQ : degree (f P) = 0 ∧ degree (f Q) = 0 := by
-      rw [← Nat.WithBot.add_eq_zero_iff, ← degree_mul, ← _root_.map_mul, hQ, map_one, degree_one]
-    have hcoeff : (f P).coeff n = 0 := by
-      refine' coeff_eq_zero_of_degree_lt _
-      rw [hPQ.1]
-      exact (@WithBot.coe_pos _ _ _ n).2 (Ne.bot_lt hn)
-    rw [coe_mapRingHom, coeff_map, ← RingHom.mem_ker, Ideal.mk_ker] at hcoeff
-    exact hcoeff
-
-/-- Let `P` be a polynomial over `R`. `P` is a unit if and only if all its coefficients are
-nilpotent, except its constant term which is a unit. -/
-theorem isUnit_iff_coeff_isUnit_isNilpotent (P : Polynomial R) :
-    IsUnit P ↔ IsUnit (P.coeff 0) ∧ (∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) :=
-  ⟨coeff_isUnit_isNilpotent_of_isUnit, fun H => isUnit_of_coeff_isUnit_isNilpotent H.1 H.2⟩
-
 end CommRing
 
 end Polynomial

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

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

@@ -887,7 +887,7 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
         dsimp
         erw [iterToSum_C_X, rename_X, rename_X]
         rfl
-    rw [← @prime_C_iff (MvPolynomial s R) (↥sᶜ) instCommRingMvPolynomialToCommSemiring p]
+    rw [← @prime_C_iff (MvPolynomial s R) (↥sᶜ) instCommRingMvPolynomial p]
     rw [@MulEquiv.prime_iff (MvPolynomial ↑sᶜ (MvPolynomial ↑s R)) (MvPolynomial σ R) (_) (_)]
     rotate_left
     exact eqv.toMulEquiv

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

@@ -871,9 +871,6 @@ set_option linter.uppercaseLean3 false in
 
 variable {σ}
 
-/- Porting note: this suffers from serious time out issues without removing
-this instance -/
-attribute [-instance] MvPolynomial.instCommRingMvPolynomialToCommSemiring in
 theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
     Prime (rename ((↑) : s → σ) p) ↔ Prime (p : MvPolynomial s R) := by
   classical

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.basic
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.CharP.Basic
 import Mathlib.Algebra.GeomSum
@@ -16,6 +11,8 @@ import Mathlib.RingTheory.Polynomial.Content
 import Mathlib.RingTheory.UniqueFactorizationDomain
 import Mathlib.RingTheory.Ideal.QuotientOperations
 
+#align_import ring_theory.polynomial.basic from "leanprover-community/mathlib"@"da420a8c6dd5bdfb85c4ced85c34388f633bc6ff"
+
 /-!
 # Ring-theoretic supplement of Data.Polynomial.
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -957,7 +957,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
           Classical.by_contradiction fun hxm =>
             haveI : IsNoetherian R R := inst
             have : ¬M < I.leadingCoeffNth k := by
-              refine' WellFounded.not_lt_min (wellFounded_submodule_gt R R) _ _ _ ; exact ⟨k, rfl⟩
+              refine' WellFounded.not_lt_min (wellFounded_submodule_gt R R) _ _ _; exact ⟨k, rfl⟩
             this ⟨HN ▸ I.leadingCoeffNth_mono (le_of_lt h), fun H => hxm (H hx)⟩
       have hs2 : ∀ {x}, x ∈ I.degreeLE N → x ∈ Ideal.span (↑s : Set R[X]) :=
         hs ▸ fun hx =>

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -498,10 +498,10 @@ theorem coeff_isUnit_isNilpotent_of_isUnit {P : Polynomial R} (hunit : IsUnit P)
     IsUnit (P.coeff 0) ∧ (∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) := by
   obtain ⟨Q, hQ⟩ := IsUnit.exists_right_inv hunit
   constructor
-  . refine' isUnit_of_mul_eq_one _ (Q.coeff 0) _
+  · refine' isUnit_of_mul_eq_one _ (Q.coeff 0) _
     have h := (mul_coeff_zero P Q).symm
     rwa [hQ, coeff_one_zero] at h
-  . intros n hn
+  · intros n hn
     rw [nilpotent_iff_mem_prime]
     intros I hI
     let f := mapRingHom (Ideal.Quotient.mk I)

We proved that a polynomial is a unit if and only if all of its coefficients are nilpotent, except the constant term which is a unit.

Co-authored-by: Cyprien Chauveau cyprien.chauveau@etu.u-paris.fr Co-authored-by: Lucas Pouillart lucas.pouillart@etu.u-paris.fr

Co-authored-by: EmilieUthaiwat <102412311+EmilieUthaiwat@users.noreply.github.com>

@@ -14,6 +14,7 @@ import Mathlib.Data.MvPolynomial.CommRing
 import Mathlib.Data.MvPolynomial.Equiv
 import Mathlib.RingTheory.Polynomial.Content
 import Mathlib.RingTheory.UniqueFactorizationDomain
+import Mathlib.RingTheory.Ideal.QuotientOperations
 
 /-!
 # Ring-theoretic supplement of Data.Polynomial.
@@ -256,6 +257,13 @@ theorem monic_geom_sum_X {n : ℕ} (hn : n ≠ 0) : (∑ i in range n, (X : R[X]
 set_option linter.uppercaseLean3 false in
 #align polynomial.monic_geom_sum_X Polynomial.monic_geom_sum_X
 
+theorem IsNilpotent.C_mul_X_pow_isNilpotent {r : R} (n : ℕ) (hnil : IsNilpotent r) :
+    IsNilpotent ((C r) * X ^ n) := by
+  refine' Commute.isNilpotent_mul_left (commute_X_pow _ _).symm _
+  obtain ⟨m, hm⟩ := hnil
+  refine' ⟨m, _⟩
+  rw [← C_pow, hm, C_0]
+
 end Semiring
 
 section Ring
@@ -460,6 +468,58 @@ theorem ker_modByMonicHom (hq : q.Monic) :
 
 end ModByMonic
 
+/-- Let `P` be a polynomial over `R`. If its constant term is a unit and its other coefficients are
+nilpotent, then `P` is a unit. -/
+theorem isUnit_of_coeff_isUnit_isNilpotent {P : Polynomial R} (hunit : IsUnit (P.coeff 0))
+    (hnil : ∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) : IsUnit P := by
+  induction' h : P.natDegree using Nat.strong_induction_on with k hind generalizing P
+  by_cases hdeg : P.natDegree = 0
+  { rw [eq_C_of_natDegree_eq_zero hdeg]
+    exact hunit.map C }
+  set P₁ := P.eraseLead with hP₁
+  suffices IsUnit P₁ by
+    rw [← eraseLead_add_monomial_natDegree_leadingCoeff P, ← C_mul_X_pow_eq_monomial]
+    obtain ⟨Q, hQ⟩ := this
+    rw [← hP₁, ← hQ]
+    refine' Commute.IsNilpotent.add_isUnit (IsNilpotent.C_mul_X_pow_isNilpotent _ (hnil _ hdeg))
+      ((Commute.all _ _).mul_left (Commute.all _ _))
+  have hdeg₂ := lt_of_le_of_lt P.eraseLead_natDegree_le (Nat.sub_lt
+    (Nat.pos_of_ne_zero hdeg) zero_lt_one)
+  refine' hind P₁.natDegree _ _ (fun i hi => _) rfl
+  · simp_rw [← h, hdeg₂]
+  · simp_rw [eraseLead_coeff_of_ne _ (Ne.symm hdeg), hunit]
+  · by_cases H : i ≤ P₁.natDegree
+    simp_rw [eraseLead_coeff_of_ne _ (ne_of_lt (lt_of_le_of_lt H hdeg₂)), hnil i hi]
+    simp_rw [coeff_eq_zero_of_natDegree_lt (lt_of_not_ge H), IsNilpotent.zero]
+
+/-- Let `P` be a polynomial over `R`. If `P` is a unit, then all its coefficients are nilpotent,
+except its constant term which is a unit. -/
+theorem coeff_isUnit_isNilpotent_of_isUnit {P : Polynomial R} (hunit : IsUnit P) :
+    IsUnit (P.coeff 0) ∧ (∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) := by
+  obtain ⟨Q, hQ⟩ := IsUnit.exists_right_inv hunit
+  constructor
+  . refine' isUnit_of_mul_eq_one _ (Q.coeff 0) _
+    have h := (mul_coeff_zero P Q).symm
+    rwa [hQ, coeff_one_zero] at h
+  . intros n hn
+    rw [nilpotent_iff_mem_prime]
+    intros I hI
+    let f := mapRingHom (Ideal.Quotient.mk I)
+    have hPQ : degree (f P) = 0 ∧ degree (f Q) = 0 := by
+      rw [← Nat.WithBot.add_eq_zero_iff, ← degree_mul, ← _root_.map_mul, hQ, map_one, degree_one]
+    have hcoeff : (f P).coeff n = 0 := by
+      refine' coeff_eq_zero_of_degree_lt _
+      rw [hPQ.1]
+      exact (@WithBot.coe_pos _ _ _ n).2 (Ne.bot_lt hn)
+    rw [coe_mapRingHom, coeff_map, ← RingHom.mem_ker, Ideal.mk_ker] at hcoeff
+    exact hcoeff
+
+/-- Let `P` be a polynomial over `R`. `P` is a unit if and only if all its coefficients are
+nilpotent, except its constant term which is a unit. -/
+theorem isUnit_iff_coeff_isUnit_isNilpotent (P : Polynomial R) :
+    IsUnit P ↔ IsUnit (P.coeff 0) ∧ (∀ i, i ≠ 0 → IsNilpotent (P.coeff i)) :=
+  ⟨coeff_isUnit_isNilpotent_of_isUnit, fun H => isUnit_of_coeff_isUnit_isNilpotent H.1 H.2⟩
+
 end CommRing
 
 end Polynomial

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -822,8 +822,8 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
   classical
     symm
     let eqv :=
-      (sumAlgEquiv R (↥(sᶜ)) s).symm.trans
-        (renameEquiv R <| (Equiv.sumComm (↥(sᶜ)) s).trans <| Equiv.Set.sumCompl s)
+      (sumAlgEquiv R (↥sᶜ) s).symm.trans
+        (renameEquiv R <| (Equiv.sumComm (↥sᶜ) s).trans <| Equiv.Set.sumCompl s)
     have : (rename (↑)).toRingHom = eqv.toAlgHom.toRingHom.comp C := by
       apply ringHom_ext
       · intro
@@ -833,8 +833,8 @@ theorem prime_rename_iff (s : Set σ) {p : MvPolynomial s R} :
         dsimp
         erw [iterToSum_C_X, rename_X, rename_X]
         rfl
-    rw [← @prime_C_iff (MvPolynomial s R) (↥(sᶜ)) instCommRingMvPolynomialToCommSemiring p]
-    rw [@MulEquiv.prime_iff (MvPolynomial (↑(sᶜ)) (MvPolynomial (↑s) R)) (MvPolynomial σ R) (_) (_)]
+    rw [← @prime_C_iff (MvPolynomial s R) (↥sᶜ) instCommRingMvPolynomialToCommSemiring p]
+    rw [@MulEquiv.prime_iff (MvPolynomial ↑sᶜ (MvPolynomial ↑s R)) (MvPolynomial σ R) (_) (_)]
     rotate_left
     exact eqv.toMulEquiv
     convert Iff.rfl

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -589,7 +589,7 @@ theorem mem_leadingCoeffNth_zero (x) : x ∈ I.leadingCoeffNth 0 ↔ C x ∈ I :
 
 theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤ I.leadingCoeffNth n := by
   intro r hr
-  simp only [SetLike.mem_coe, mem_leadingCoeffNth] at hr⊢
+  simp only [SetLike.mem_coe, mem_leadingCoeffNth] at hr ⊢
   rcases hr with ⟨p, hpI, hpdeg, rfl⟩
   refine' ⟨p * X ^ (n - m), I.mul_mem_right _ hpI, _, leadingCoeff_mul_X_pow⟩
   refine' le_trans (degree_mul_le _ _) _
@@ -755,7 +755,7 @@ theorem prime_C_iff : Prime (C r) ↔ Prime r :=
   ⟨comap_prime C (evalRingHom (0 : R)) fun r => eval_C, by
     intro hr
     have := hr.1
-    rw [← Ideal.span_singleton_prime] at hr⊢
+    rw [← Ideal.span_singleton_prime] at hr ⊢
     · rw [← Set.image_singleton, ← Ideal.map_span]
       apply Ideal.isPrime_map_C_of_isPrime hr
     · intro h; apply (this (C_eq_zero.mp h))

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

@@ -1212,7 +1212,7 @@ namespace Polynomial
 
 attribute [-instance] Ring.toSemiring in
 instance (priority := 100) uniqueFactorizationMonoid : UniqueFactorizationMonoid D[X] := by
-  haveI : NormalizationMonoid D:= Inhabited.default
+  haveI : NormalizationMonoid D := Inhabited.default
   haveI := toNormalizedGCDMonoid D
   exact ufm_of_gcd_of_wfDvdMonoid
 #align polynomial.unique_factorization_monoid Polynomial.uniqueFactorizationMonoid

@@ -54,12 +54,12 @@ variable (R)
 
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree ≤ `n`. -/
 def degreeLE (n : WithBot ℕ) : Submodule R R[X] :=
-  ⨅ k : ℕ, ⨅ _h : ↑k > n, LinearMap.ker (lcoeff R k)
+  ⨅ k : ℕ, ⨅ _ : ↑k > n, LinearMap.ker (lcoeff R k)
 #align polynomial.degree_le Polynomial.degreeLE
 
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree < `n`. -/
 def degreeLT (n : ℕ) : Submodule R R[X] :=
-  ⨅ k : ℕ, ⨅ (_h : k ≥ n), LinearMap.ker (lcoeff R k)
+  ⨅ k : ℕ, ⨅ (_ : k ≥ n), LinearMap.ker (lcoeff R k)
 #align polynomial.degree_lt Polynomial.degreeLT
 
 variable {R}

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -447,15 +447,15 @@ section ModByMonic
 
 variable {q : R[X]}
 
-theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} :
+theorem mem_ker_modByMonic (hq : q.Monic) {p : R[X]} :
     p ∈ LinearMap.ker (modByMonicHom q) ↔ q ∣ p :=
   LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
-#align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monic
+#align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_modByMonic
 
 @[simp]
 theorem ker_modByMonicHom (hq : q.Monic) :
     LinearMap.ker (Polynomial.modByMonicHom q) = (Ideal.span {q}).restrictScalars R :=
-  Submodule.ext fun _ => (mem_ker_mod_by_monic hq).trans Ideal.mem_span_singleton.symm
+  Submodule.ext fun _ => (mem_ker_modByMonic hq).trans Ideal.mem_span_singleton.symm
 #align polynomial.ker_mod_by_monic_hom Polynomial.ker_modByMonicHom
 
 end ModByMonic

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -447,15 +447,11 @@ section ModByMonic
 
 variable {q : R[X]}
 
--- Porting note: failed to synthesize semilinearmapclass on modByMonic
-set_option synthInstance.etaExperiment true in
 theorem mem_ker_mod_by_monic (hq : q.Monic) {p : R[X]} :
     p ∈ LinearMap.ker (modByMonicHom q) ↔ q ∣ p :=
   LinearMap.mem_ker.trans (dvd_iff_modByMonic_eq_zero hq)
 #align polynomial.mem_ker_mod_by_monic Polynomial.mem_ker_mod_by_monic
 
--- Porting note: failed to synthesize semilinearmapclass on modByMonic
-set_option synthInstance.etaExperiment true in
 @[simp]
 theorem ker_modByMonicHom (hq : q.Monic) :
     LinearMap.ker (Polynomial.modByMonicHom q) = (Ideal.span {q}).restrictScalars R :=
@@ -551,9 +547,6 @@ theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
 set_option linter.uppercaseLean3 false in
 #align ideal.mem_map_C_iff Ideal.mem_map_C_iff
 
-
--- Porting note: failed to synthesize semilinearmapclass on modByMonic
--- set_option synthInstance.etaExperiment true in fails
 theorem _root_.Polynomial.ker_mapRingHom (f : R →+* S) :
     LinearMap.ker (Polynomial.mapRingHom f).toSemilinearMap = f.ker.map (C : R →+* R[X]) := by
   ext
@@ -672,8 +665,6 @@ section CommRing
 
 variable [CommRing R]
 
--- Porting note: failed to synthesize semilinearmapclass on modByMonic
-set_option synthInstance.etaExperiment true in
 /-- If `P` is a prime ideal of `R`, then `P.R[x]` is a prime ideal of `R[x]`. -/
 theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) ↔ IsPrime P := by
@@ -891,7 +882,6 @@ instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R
 
 end Polynomial
 
-set_option synthInstance.etaExperiment true in
 /-- Hilbert basis theorem: a polynomial ring over a noetherian ring is a noetherian ring. -/
 protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNoetherianRing R[X] :=
   isNoetherianRing_iff.2
@@ -993,8 +983,6 @@ theorem exists_irreducible_of_natDegree_ne_zero {R : Type u} [CommRing R] [IsDom
   exists_irreducible_of_natDegree_pos <| Nat.pos_of_ne_zero hf
 #align polynomial.exists_irreducible_of_nat_degree_ne_zero Polynomial.exists_irreducible_of_natDegree_ne_zero
 
--- Porting note: failed to synthesize  HPow (M →ₗ[R] M) ℕ ?m
-set_option synthInstance.etaExperiment true in
 theorem linearIndependent_powers_iff_aeval (f : M →ₗ[R] M) (v : M) :
     (LinearIndependent R fun n : ℕ => (f ^ n) v) ↔ ∀ p : R[X], aeval f p v = 0 → p = 0 := by
   rw [linearIndependent_iff]

Please refer to this Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Naming.20convention/near/357712556

@@ -739,7 +739,7 @@ set_option linter.uppercaseLean3 false in
 #align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrime
 
 theorem is_fg_degreeLE [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
-    Submodule.Fg (I.degreeLE n) :=
+    Submodule.FG (I.degreeLE n) :=
   isNoetherian_submodule_left.1
     -- porting note: times out without explicit `R`.
     (isNoetherian_of_fg_of_noetherian _ ⟨_, (degreeLE_eq_span_X_pow (R := R)).symm⟩) _

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

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

@@ -65,7 +65,7 @@ def degreeLT (n : ℕ) : Submodule R R[X] :=
 variable {R}
 
 theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degree f ≤ n := by
-  simp only [degreeLE, Submodule.mem_infᵢ, degree_le_iff_coeff_zero, LinearMap.mem_ker]; rfl
+  simp only [degreeLE, Submodule.mem_iInf, degree_le_iff_coeff_zero, LinearMap.mem_ker]; rfl
 #align polynomial.mem_degree_le Polynomial.mem_degreeLE
 
 @[mono]
@@ -96,8 +96,8 @@ set_option linter.uppercaseLean3 false in
 #align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLE_eq_span_X_pow
 
 theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n := by
-  rw [degreeLT, Submodule.mem_infᵢ]
-  conv_lhs => intro i; rw [Submodule.mem_infᵢ]
+  rw [degreeLT, Submodule.mem_iInf]
+  conv_lhs => intro i; rw [Submodule.mem_iInf]
   rw [degree, Finset.max_eq_sup_coe]
   rw [Finset.sup_lt_iff ?_]
   rotate_left
@@ -606,7 +606,7 @@ theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤
 #align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_mono
 
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x := by
-  rw [leadingCoeff, Submodule.mem_supᵢ_of_directed]
+  rw [leadingCoeff, Submodule.mem_iSup_of_directed]
   simp only [mem_leadingCoeffNth]
   · constructor
     · rintro ⟨i, p, hpI, _, rfl⟩

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

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

@@ -715,8 +715,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
         rintro ⟨i, j⟩ hij
         rw [Finset.mem_erase, Finset.Nat.mem_antidiagonal] at hij
         simp only [Ne.def, Prod.mk.inj_iff, not_and_or] at hij
-        obtain hi | hj : i < m ∨ j < n :=
-          by
+        obtain hi | hj : i < m ∨ j < n := by
           rw [or_iff_not_imp_left, not_lt, le_iff_lt_or_eq]
           rintro (hmi | rfl)
           · rw [← not_le]
@@ -914,72 +913,62 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
         hs ▸ fun hx =>
           Submodule.span_induction hx (fun _ hx => Ideal.subset_span hx) (Ideal.zero_mem _)
             (fun _ _ => Ideal.add_mem _) fun c f hf => f.C_mul' c ▸ Ideal.mul_mem_left _ _ hf
-      ⟨s,
-        le_antisymm
-            (Ideal.span_le.2 fun x hx =>
-              have : x ∈ I.degreeLE N := hs ▸ Submodule.subset_span hx
-              this.2) <|
-          by
-          have : Submodule.span R[X] ↑s = Ideal.span ↑s := by rfl
-          rw [this]
-          intro p hp
-          generalize hn : p.natDegree = k
-          induction' k using Nat.strong_induction_on with k ih generalizing p
-          cases' le_or_lt k N with h h
-          · subst k
-            refine'
-              hs2
-                ⟨Polynomial.mem_degreeLE.2
-                    (le_trans Polynomial.degree_le_natDegree <| WithBot.coe_le_coe.2 h),
-                  hp⟩
-          · have hp0 : p ≠ 0 := by
-              rintro rfl
-              cases hn
-              exact Nat.not_lt_zero _ h
-            have : (0 : R) ≠ 1 := by
-              intro h
-              apply hp0
-              ext i
-              refine' (mul_one _).symm.trans _
-              rw [← h, MulZeroClass.mul_zero]
-              rfl
-            haveI : Nontrivial R := ⟨⟨0, 1, this⟩⟩
-            have : p.leadingCoeff ∈ I.leadingCoeffNth N :=
-              by
-              rw [HN]
-              exact
-                hm2 k
-                  ((I.mem_leadingCoeffNth _ _).2
-                    ⟨_, hp, hn ▸ Polynomial.degree_le_natDegree, rfl⟩)
-            rw [I.mem_leadingCoeffNth] at this
-            rcases this with ⟨q, hq, hdq, hlqp⟩
-            have hq0 : q ≠ 0 := by
-              intro H
-              rw [← Polynomial.leadingCoeff_eq_zero] at H
-              rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H
-              exact hp0 H
-            have h1 : p.degree = (q * Polynomial.X ^ (k - q.natDegree)).degree :=
-              by
-              rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
-              rw [Polynomial.degree_eq_natDegree hp0, Polynomial.degree_eq_natDegree hq0]
-              rw [Nat.cast_withBot, Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add,
-                add_tsub_cancel_of_le, hn]
-              · refine' le_trans (Polynomial.natDegree_le_of_degree_le hdq) (le_of_lt h)
-              rw [Polynomial.leadingCoeff_X_pow, mul_one]
-              exact mt Polynomial.leadingCoeff_eq_zero.1 hq0
-            have h2 : p.leadingCoeff = (q * Polynomial.X ^ (k - q.natDegree)).leadingCoeff := by
-              rw [← hlqp, Polynomial.leadingCoeff_mul_X_pow]
-            have := Polynomial.degree_sub_lt h1 hp0 h2
-            rw [Polynomial.degree_eq_natDegree hp0] at this
-            rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.natDegree))]
-            refine' (Ideal.span ↑s).add_mem _ ((Ideal.span ↑s).mul_mem_right _ _)
-            · by_cases hpq : p - q * Polynomial.X ^ (k - q.natDegree) = 0
-              · rw [hpq]
-                exact Ideal.zero_mem _
-              refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
-              rwa [Polynomial.degree_eq_natDegree hpq, Nat.cast_withBot, Nat.cast_withBot,
-                WithBot.coe_lt_coe, hn] at this
-            exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
+      ⟨s, le_antisymm (Ideal.span_le.2 fun x hx =>
+          have : x ∈ I.degreeLE N := hs ▸ Submodule.subset_span hx
+          this.2) <| by
+        have : Submodule.span R[X] ↑s = Ideal.span ↑s := by rfl
+        rw [this]
+        intro p hp
+        generalize hn : p.natDegree = k
+        induction' k using Nat.strong_induction_on with k ih generalizing p
+        cases' le_or_lt k N with h h
+        · subst k
+          refine' hs2 ⟨Polynomial.mem_degreeLE.2
+            (le_trans Polynomial.degree_le_natDegree <| WithBot.coe_le_coe.2 h), hp⟩
+        · have hp0 : p ≠ 0 := by
+            rintro rfl
+            cases hn
+            exact Nat.not_lt_zero _ h
+          have : (0 : R) ≠ 1 := by
+            intro h
+            apply hp0
+            ext i
+            refine' (mul_one _).symm.trans _
+            rw [← h, MulZeroClass.mul_zero]
+            rfl
+          haveI : Nontrivial R := ⟨⟨0, 1, this⟩⟩
+          have : p.leadingCoeff ∈ I.leadingCoeffNth N := by
+            rw [HN]
+            exact hm2 k ((I.mem_leadingCoeffNth _ _).2
+              ⟨_, hp, hn ▸ Polynomial.degree_le_natDegree, rfl⟩)
+          rw [I.mem_leadingCoeffNth] at this
+          rcases this with ⟨q, hq, hdq, hlqp⟩
+          have hq0 : q ≠ 0 := by
+            intro H
+            rw [← Polynomial.leadingCoeff_eq_zero] at H
+            rw [hlqp, Polynomial.leadingCoeff_eq_zero] at H
+            exact hp0 H
+          have h1 : p.degree = (q * Polynomial.X ^ (k - q.natDegree)).degree := by
+            rw [Polynomial.degree_mul', Polynomial.degree_X_pow]
+            rw [Polynomial.degree_eq_natDegree hp0, Polynomial.degree_eq_natDegree hq0]
+            rw [Nat.cast_withBot, Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add,
+              add_tsub_cancel_of_le, hn]
+            · refine' le_trans (Polynomial.natDegree_le_of_degree_le hdq) (le_of_lt h)
+            rw [Polynomial.leadingCoeff_X_pow, mul_one]
+            exact mt Polynomial.leadingCoeff_eq_zero.1 hq0
+          have h2 : p.leadingCoeff = (q * Polynomial.X ^ (k - q.natDegree)).leadingCoeff := by
+            rw [← hlqp, Polynomial.leadingCoeff_mul_X_pow]
+          have := Polynomial.degree_sub_lt h1 hp0 h2
+          rw [Polynomial.degree_eq_natDegree hp0] at this
+          rw [← sub_add_cancel p (q * Polynomial.X ^ (k - q.natDegree))]
+          refine' (Ideal.span ↑s).add_mem _ ((Ideal.span ↑s).mul_mem_right _ _)
+          · by_cases hpq : p - q * Polynomial.X ^ (k - q.natDegree) = 0
+            · rw [hpq]
+              exact Ideal.zero_mem _
+            refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
+            rwa [Polynomial.degree_eq_natDegree hpq, Nat.cast_withBot, Nat.cast_withBot,
+              WithBot.coe_lt_coe, hn] at this
+          exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
 #align polynomial.is_noetherian_ring Polynomial.isNoetherianRing
 
 attribute [instance] Polynomial.isNoetherianRing
@@ -1098,8 +1087,8 @@ theorem isNoetherianRing_fin [IsNoetherianRing R] :
 
 /-- The multivariate polynomial ring in finitely many variables over a noetherian ring
 is itself a noetherian ring. -/
-instance isNoetherianRing [Finite σ] [IsNoetherianRing R] : IsNoetherianRing (MvPolynomial σ R) :=
-  by
+instance isNoetherianRing [Finite σ] [IsNoetherianRing R] :
+    IsNoetherianRing (MvPolynomial σ R) := by
   cases nonempty_fintype σ
   exact
     @isNoetherianRing_of_ringEquiv (MvPolynomial (Fin (Fintype.card σ)) R) _ _ _
@@ -1138,13 +1127,11 @@ instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
     obtain ⟨s, p, rfl⟩ := exists_finset_rename p
     obtain ⟨t, q, rfl⟩ := exists_finset_rename q
     have :
-      rename (Subtype.map id (Finset.subset_union_left s t) : { x // x ∈ s } → { x // x ∈ s ∪ t })
-            p *
-          rename
-            (Subtype.map id (Finset.subset_union_right s t) : { x // x ∈ t } → { x // x ∈ s ∪ t })
-            q =
-        0 :=
-      by
+        rename (Subtype.map id (Finset.subset_union_left s t) :
+          { x // x ∈ s } → { x // x ∈ s ∪ t }) p *
+        rename (Subtype.map id (Finset.subset_union_right s t) :
+          { x // x ∈ t } → { x // x ∈ s ∪ t }) q =
+        0 := by
       apply rename_injective _ Subtype.val_injective
       simpa using h
     letI that := MvPolynomial.noZeroDivisors_of_finite R { x // x ∈ s ∪ t }

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

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

@@ -892,6 +892,7 @@ instance (priority := 100) {R : Type _} [CommRing R] [IsDomain R] [WfDvdMonoid R
 
 end Polynomial
 
+set_option synthInstance.etaExperiment true in
 /-- Hilbert basis theorem: a polynomial ring over a noetherian ring is a noetherian ring. -/
 protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNoetherianRing R[X] :=
   isNoetherianRing_iff.2

@@ -80,7 +80,6 @@ theorem degreeLE_eq_span_X_pow {n : ℕ} :
     replace hp := mem_degreeLE.1 hp
     rw [← Polynomial.sum_monomial_eq p, Polynomial.sum]
     refine' Submodule.sum_mem _ fun k hk => _
-    show monomial _ _ ∈ _
     have := WithBot.coe_le_coe.1 (Finset.sup_le_iff.1 hp k hk)
     rw [← C_mul_X_pow_eq_monomial, C_mul']
     refine'
@@ -89,7 +88,8 @@ theorem degreeLE_eq_span_X_pow {n : ℕ} :
           Finset.mem_coe.2 <|
             Finset.mem_image.2 ⟨_, Finset.mem_range.2 (Nat.lt_succ_of_le this), rfl⟩)
   rw [Submodule.span_le, Finset.coe_image, Set.image_subset_iff]
-  intro k hk; apply mem_degreeLE.2
+  intro k hk
+  apply mem_degreeLE.2
   exact
     (degree_X_pow_le _).trans (WithBot.coe_le_coe.2 <| Nat.le_of_lt_succ <| Finset.mem_range.1 hk)
 set_option linter.uppercaseLean3 false in
@@ -104,8 +104,8 @@ theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n
   apply WithBot.bot_lt_coe
   conv_rhs =>
     simp only [mem_support_iff]
-    intro b; rw [Nat.cast_withBot, WithBot.coe_lt_coe, lt_iff_not_le]
-    change ¬ coeff f b = 0 → ¬ n ≤ b; rw [not_imp_not]
+    intro b
+    rw [Nat.cast_withBot, WithBot.coe_lt_coe, lt_iff_not_le, Ne, not_imp_not]
 #align polynomial.mem_degree_lt Polynomial.mem_degreeLT
 
 @[mono]
@@ -120,7 +120,6 @@ theorem degreeLT_eq_span_X_pow {n : ℕ} :
     replace hp := mem_degreeLT.1 hp
     rw [← Polynomial.sum_monomial_eq p, Polynomial.sum]
     refine' Submodule.sum_mem _ fun k hk => _
-    show monomial _ _ ∈ _
     have := WithBot.coe_lt_coe.1 ((Finset.sup_lt_iff <| WithBot.bot_lt_coe n).1 hp k hk)
     rw [← C_mul_X_pow_eq_monomial, C_mul']
     refine'
@@ -128,7 +127,8 @@ theorem degreeLT_eq_span_X_pow {n : ℕ} :
         (Submodule.subset_span <|
           Finset.mem_coe.2 <| Finset.mem_image.2 ⟨_, Finset.mem_range.2 this, rfl⟩)
   rw [Submodule.span_le, Finset.coe_image, Set.image_subset_iff]
-  intro k hk; apply mem_degreeLT.2
+  intro k hk
+  apply mem_degreeLT.2
   exact lt_of_le_of_lt (degree_X_pow_le _) (WithBot.coe_lt_coe.2 <| Finset.mem_range.1 hk)
 set_option linter.uppercaseLean3 false in
 #align polynomial.degree_lt_eq_span_X_pow Polynomial.degreeLT_eq_span_X_pow
@@ -151,7 +151,8 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
     rw [coeff_smul]
     rfl
   left_inv := by
-    rintro ⟨p, hp⟩; ext1
+    rintro ⟨p, hp⟩
+    ext1
     simp only [Submodule.coe_mk]
     by_cases hp0 : p = 0
     · subst hp0
@@ -159,8 +160,8 @@ def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n →
     rw [mem_degreeLT, degree_eq_natDegree hp0,
       Nat.cast_withBot, Nat.cast_withBot, WithBot.coe_lt_coe] at hp
     conv_rhs => rw [p.as_sum_range' n hp, ← Fin.sum_univ_eq_sum_range]
-  right_inv := by
-    intro f; ext i
+  right_inv f := by
+    ext i
     simp only [finset_sum_coeff, Submodule.coe_mk]
     rw [Finset.sum_eq_single i, coeff_monomial, if_pos rfl]
     · rintro j - hji
@@ -230,18 +231,17 @@ set_option linter.uppercaseLean3 false in
 theorem Monic.geom_sum {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.natDegree) {n : ℕ} (hn : n ≠ 0) :
     (∑ i in range n, P ^ i).Monic := by
   nontriviality R
-  cases' n with n;
-  · exact (hn rfl).elim
-  · rw [geom_sum_succ']
-    refine' (hP.pow _).add_of_left _
-    refine' lt_of_le_of_lt (degree_sum_le _ _) _
-    rw [Finset.sup_lt_iff]
-    · simp only [Finset.mem_range, degree_eq_natDegree (hP.pow _).ne_zero]
-      simp only [Nat.cast_withBot, WithBot.coe_lt_coe, hP.natDegree_pow]
-      intro k
-      exact nsmul_lt_nsmul hdeg
-    · rw [bot_lt_iff_ne_bot, Ne.def, degree_eq_bot]
-      exact (hP.pow _).ne_zero
+  obtain ⟨n, rfl⟩ := Nat.exists_eq_succ_of_ne_zero hn
+  rw [geom_sum_succ']
+  refine' (hP.pow _).add_of_left _
+  refine' lt_of_le_of_lt (degree_sum_le _ _) _
+  rw [Finset.sup_lt_iff]
+  · simp only [Finset.mem_range, degree_eq_natDegree (hP.pow _).ne_zero]
+    simp only [Nat.cast_withBot, WithBot.coe_lt_coe, hP.natDegree_pow]
+    intro k
+    exact nsmul_lt_nsmul hdeg
+  · rw [bot_lt_iff_ne_bot, Ne.def, degree_eq_bot]
+    exact (hP.pow _).ne_zero
 #align polynomial.monic.geom_sum Polynomial.Monic.geom_sum
 
 theorem Monic.geom_sum' {P : R[X]} (hP : P.Monic) (hdeg : 0 < P.degree) {n : ℕ} (hn : n ≠ 0) :
@@ -277,7 +277,7 @@ def restriction (p : R[X]) : Polynomial (Subring.closure (↑p.frange : Set R))
 theorem coeff_restriction {p : R[X]} {n : ℕ} : ↑(coeff (restriction p) n) = coeff p n := by
   simp only [restriction, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
     Ne.def, ite_not]
-  split_ifs; rename_i h
+  split_ifs with h
   · rw [h]
     rfl
   · rfl
@@ -293,10 +293,7 @@ theorem support_restriction (p : R[X]) : support (restriction p) = support p :=
   ext i
   simp only [mem_support_iff, not_iff_not, Ne.def]
   conv_rhs => rw [← coeff_restriction]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H, ZeroMemClass.coe_zero], fun H => Subtype.coe_injective H⟩
 #align polynomial.support_restriction Polynomial.support_restriction
 
 @[simp]
@@ -318,10 +315,7 @@ theorem natDegree_restriction {p : R[X]} : (restriction p).natDegree = p.natDegr
 theorem monic_restriction {p : R[X]} : Monic (restriction p) ↔ Monic p := by
   simp only [Monic, leadingCoeff, natDegree_restriction]
   rw [← @coeff_restriction _ _ p]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H, OneMemClass.coe_one], fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_restriction Polynomial.monic_restriction
 
 @[simp]
@@ -339,8 +333,8 @@ variable [Semiring S] {f : R →+* S} {x : S}
 theorem eval₂_restriction {p : R[X]} :
     eval₂ f x p =
       eval₂ (f.comp (Subring.subtype (Subring.closure (p.frange : Set R)))) x p.restriction := by
-  simp only [eval₂_eq_sum, sum, support_restriction, ← @coeff_restriction _ _ p]
-  rfl
+  simp only [eval₂_eq_sum, sum, support_restriction, ← @coeff_restriction _ _ p, RingHom.comp_apply,
+    Subring.coeSubtype]
 #align polynomial.eval₂_restriction Polynomial.eval₂_restriction
 
 section ToSubring
@@ -362,26 +356,23 @@ variable (hp : (↑p.frange : Set R) ⊆ T)
 theorem coeff_toSubring {n : ℕ} : ↑(coeff (toSubring p T hp) n) = coeff p n := by
   simp only [toSubring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
     Ne.def, ite_not]
-  split_ifs; rename_i h
+  split_ifs with h
   · rw [h]
     rfl
   · rfl
 #align polynomial.coeff_to_subring Polynomial.coeff_toSubring
 
 -- Porting note: removed @[simp] as simp can prove this
-theorem coeff_to_subring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
+theorem coeff_toSubring' {n : ℕ} : (coeff (toSubring p T hp) n).1 = coeff p n :=
   coeff_toSubring _ _ hp
-#align polynomial.coeff_to_subring' Polynomial.coeff_to_subring'
+#align polynomial.coeff_to_subring' Polynomial.coeff_toSubring'
 
 @[simp]
 theorem support_toSubring : support (toSubring p T hp) = support p := by
   ext i
   simp only [mem_support_iff, not_iff_not, Ne.def]
   conv_rhs => rw [← coeff_toSubring p T hp]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H, ZeroMemClass.coe_zero], fun H => Subtype.coe_injective H⟩
 #align polynomial.support_to_subring Polynomial.support_toSubring
 
 @[simp]
@@ -395,10 +386,7 @@ theorem natDegree_toSubring : (toSubring p T hp).natDegree = p.natDegree := by s
 @[simp]
 theorem monic_toSubring : Monic (toSubring p T hp) ↔ Monic p := by
   simp_rw [Monic, leadingCoeff, natDegree_toSubring, ← coeff_toSubring p T hp]
-  exact
-    ⟨fun H => by
-      rw [H]
-      rfl, fun H => Subtype.coe_injective H⟩
+  exact ⟨fun H => by rw [H, OneMemClass.coe_one], fun H => Subtype.coe_injective H⟩
 #align polynomial.monic_to_subring Polynomial.monic_toSubring
 
 @[simp]
@@ -412,7 +400,9 @@ theorem toSubring_one :
     toSubring (1 : R[X]) T
         (Set.Subset.trans frange_one <| Finset.singleton_subset_set_iff.2 T.one_mem) =
       1 :=
-  ext fun i => Subtype.eq <| by rw [coeff_to_subring', coeff_one, coeff_one]; split_ifs <;> rfl
+  ext fun i => Subtype.eq <| by
+    rw [coeff_toSubring', coeff_one, coeff_one, apply_ite Subtype.val, ZeroMemClass.coe_zero,
+      OneMemClass.coe_one]
 #align polynomial.to_subring_one Polynomial.toSubring_one
 
 @[simp]
@@ -435,8 +425,7 @@ theorem coeff_ofSubring (p : T[X]) (n : ℕ) : coeff (ofSubring T p) n = (coeff
   simp only [ofSubring, coeff_monomial, finset_sum_coeff, mem_support_iff, Finset.sum_ite_eq',
     ite_eq_right_iff, Ne.def, ite_not, Classical.not_not, ite_eq_left_iff]
   intro h
-  rw [h]
-  rfl
+  rw [h, ZeroMemClass.coe_zero]
 #align polynomial.coeff_of_subring Polynomial.coeff_ofSubring
 
 @[simp]
@@ -488,8 +477,7 @@ section Semiring
 variable [Semiring R]
 
 /-- Transport an ideal of `R[X]` to an `R`-submodule of `R[X]`. -/
-def ofPolynomial (I : Ideal R[X]) : Submodule R R[X]
-    where
+def ofPolynomial (I : Ideal R[X]) : Submodule R R[X] where
   carrier := I.carrier
   zero_mem' := I.zero_mem
   add_mem' := I.add_mem
@@ -546,7 +534,7 @@ theorem mem_map_C_iff {I : Ideal R} {f : R[X]} :
     · intro f hf n
       cases' (Set.mem_image _ _ _).mp hf with x hx
       rw [← hx.right, coeff_C]
-      by_cases n = 0
+      by_cases h : n = 0
       · simpa [h] using hx.left
       · simp [h]
     · simp
@@ -587,16 +575,14 @@ theorem mem_leadingCoeffNth (n : ℕ) (x) :
       rw [leadingCoeff_zero, eq_comm]
       exact coeff_eq_zero_of_degree_lt hpdeg
     · refine' ⟨p, hpI, le_of_eq hpdeg, _⟩
-      rw [Polynomial.leadingCoeff, natDegree, hpdeg]
-      rfl
+      rw [Polynomial.leadingCoeff, natDegree, hpdeg, Nat.cast_withBot, WithBot.unbot'_coe]
   · rintro ⟨p, hpI, hpdeg, rfl⟩
     have : natDegree p + (n - natDegree p) = n :=
       add_tsub_cancel_of_le (natDegree_le_of_degree_le hpdeg)
     refine' ⟨p * X ^ (n - natDegree p), ⟨_, I.mul_mem_right _ hpI⟩, _⟩
     · apply le_trans (degree_mul_le _ _) _
       apply le_trans (add_le_add degree_le_natDegree (degree_X_pow_le _)) _
-      rw [Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add, this]
-      exact le_rfl
+      rw [Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add, this, Nat.cast_withBot]
     · rw [Polynomial.leadingCoeff, ← coeff_mul_X_pow p (n - natDegree p), this]
 #align ideal.mem_leading_coeff_nth Ideal.mem_leadingCoeffNth
 
@@ -615,8 +601,8 @@ theorem leadingCoeffNth_mono {m n : ℕ} (H : m ≤ n) : I.leadingCoeffNth m ≤
   refine' ⟨p * X ^ (n - m), I.mul_mem_right _ hpI, _, leadingCoeff_mul_X_pow⟩
   refine' le_trans (degree_mul_le _ _) _
   refine' le_trans (add_le_add hpdeg (degree_X_pow_le _)) _
-  rw [Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add, add_tsub_cancel_of_le H]
-  exact le_rfl
+  rw [Nat.cast_withBot, Nat.cast_withBot, ← WithBot.coe_add, add_tsub_cancel_of_le H,
+    Nat.cast_withBot]
 #align ideal.leading_coeff_nth_mono Ideal.leadingCoeffNth_mono
 
 theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.leadingCoeff p = x := by
@@ -627,7 +613,7 @@ theorem mem_leadingCoeff (x) : x ∈ I.leadingCoeff ↔ ∃ p ∈ I, Polynomial.
       exact ⟨p, hpI, rfl⟩
     rintro ⟨p, hpI, rfl⟩
     exact ⟨natDegree p, p, hpI, degree_le_natDegree, rfl⟩
-  intro i j;
+  intro i j
   exact
     ⟨i + j, I.leadingCoeffNth_mono (Nat.le_add_right _ _),
       I.leadingCoeffNth_mono (Nat.le_add_left _ _)⟩
@@ -665,10 +651,7 @@ theorem polynomial_not_isField : ¬IsField R[X] := by
   nontriviality R
   intro hR
   obtain ⟨p, hp⟩ := hR.mul_inv_cancel X_ne_zero
-  have hp0 : p ≠ 0 := by
-    rintro rfl
-    rw [MulZeroClass.mul_zero] at hp
-    exact zero_ne_one hp
+  have hp0 : p ≠ 0 := right_ne_zero_of_mul_eq_one hp
   have := degree_lt_degree_mul_X hp0
   rw [← X_mul, congr_arg degree hp, degree_one, Nat.WithBot.lt_zero_iff, degree_eq_bot] at this
   exact hp0 this
@@ -1116,10 +1099,10 @@ theorem isNoetherianRing_fin [IsNoetherianRing R] :
 is itself a noetherian ring. -/
 instance isNoetherianRing [Finite σ] [IsNoetherianRing R] : IsNoetherianRing (MvPolynomial σ R) :=
   by
-  cases nonempty_fintype σ;
-    exact
-      @isNoetherianRing_of_ringEquiv (MvPolynomial (Fin (Fintype.card σ)) R) _ _ _
-        (renameEquiv R (Fintype.equivFin σ).symm).toRingEquiv isNoetherianRing_fin
+  cases nonempty_fintype σ
+  exact
+    @isNoetherianRing_of_ringEquiv (MvPolynomial (Fin (Fintype.card σ)) R) _ _ _
+      (renameEquiv R (Fintype.equivFin σ).symm).toRingEquiv isNoetherianRing_fin
 #align mv_polynomial.is_noetherian_ring MvPolynomial.isNoetherianRing
 
 /-- Auxiliary lemma:
@@ -1165,8 +1148,7 @@ instance {R : Type u} [CommSemiring R] [NoZeroDivisors R] {σ : Type v} :
       simpa using h
     letI that := MvPolynomial.noZeroDivisors_of_finite R { x // x ∈ s ∪ t }
     rw [mul_eq_zero] at this
-    cases' this with that that <;> [left, right]
-    all_goals simpa using congr_arg (rename Subtype.val) that⟩
+    apply this.imp <;> intro that <;> simpa using congr_arg (rename Subtype.val) that⟩
 
 /-- The multivariate polynomial ring over an integral domain is an integral domain. -/
 instance {R : Type u} {σ : Type v} [CommRing R] [IsDomain R] :
@@ -1212,7 +1194,7 @@ theorem mem_map_C_iff {I : Ideal R} {f : MvPolynomial σ R} :
     · intro f hf n
       cases' (Set.mem_image _ _ _).mp hf with x hx
       rw [← hx.right, coeff_C]
-      by_cases n = 0
+      by_cases h : n = 0
       · simpa [h] using hx.left
       · simp [Ne.symm h]
     · simp

@@ -53,31 +53,31 @@ instance (p : ℕ) [h : CharP R p] : CharP R[X] p :=
 variable (R)
 
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree ≤ `n`. -/
-def degreeLe (n : WithBot ℕ) : Submodule R R[X] :=
+def degreeLE (n : WithBot ℕ) : Submodule R R[X] :=
   ⨅ k : ℕ, ⨅ _h : ↑k > n, LinearMap.ker (lcoeff R k)
-#align polynomial.degree_le Polynomial.degreeLe
+#align polynomial.degree_le Polynomial.degreeLE
 
 /-- The `R`-submodule of `R[X]` consisting of polynomials of degree < `n`. -/
-def degreeLt (n : ℕ) : Submodule R R[X] :=
+def degreeLT (n : ℕ) : Submodule R R[X] :=
   ⨅ k : ℕ, ⨅ (_h : k ≥ n), LinearMap.ker (lcoeff R k)
-#align polynomial.degree_lt Polynomial.degreeLt
+#align polynomial.degree_lt Polynomial.degreeLT
 
 variable {R}
 
-theorem mem_degreeLe {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLe R n ↔ degree f ≤ n := by
-  simp only [degreeLe, Submodule.mem_infᵢ, degree_le_iff_coeff_zero, LinearMap.mem_ker]; rfl
-#align polynomial.mem_degree_le Polynomial.mem_degreeLe
+theorem mem_degreeLE {n : WithBot ℕ} {f : R[X]} : f ∈ degreeLE R n ↔ degree f ≤ n := by
+  simp only [degreeLE, Submodule.mem_infᵢ, degree_le_iff_coeff_zero, LinearMap.mem_ker]; rfl
+#align polynomial.mem_degree_le Polynomial.mem_degreeLE
 
 @[mono]
-theorem degreeLe_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLe R m ≤ degreeLe R n := fun _ hf =>
-  mem_degreeLe.2 (le_trans (mem_degreeLe.1 hf) H)
-#align polynomial.degree_le_mono Polynomial.degreeLe_mono
+theorem degreeLE_mono {m n : WithBot ℕ} (H : m ≤ n) : degreeLE R m ≤ degreeLE R n := fun _ hf =>
+  mem_degreeLE.2 (le_trans (mem_degreeLE.1 hf) H)
+#align polynomial.degree_le_mono Polynomial.degreeLE_mono
 
-theorem degreeLe_eq_span_X_pow {n : ℕ} :
-    degreeLe R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) := by
+theorem degreeLE_eq_span_X_pow {n : ℕ} :
+    degreeLE R n = Submodule.span R ↑((Finset.range (n + 1)).image fun n => (X : R[X]) ^ n) := by
   apply le_antisymm
   · intro p hp
-    replace hp := mem_degreeLe.1 hp
+    replace hp := mem_degreeLE.1 hp
     rw [← Polynomial.sum_monomial_eq p, Polynomial.sum]
     refine' Submodule.sum_mem _ fun k hk => _
     show monomial _ _ ∈ _
@@ -89,14 +89,14 @@ theorem degreeLe_eq_span_X_pow {n : ℕ} :
           Finset.mem_coe.2 <|
             Finset.mem_image.2 ⟨_, Finset.mem_range.2 (Nat.lt_succ_of_le this), rfl⟩)
   rw [Submodule.span_le, Finset.coe_image, Set.image_subset_iff]
-  intro k hk; apply mem_degreeLe.2
+  intro k hk; apply mem_degreeLE.2
   exact
     (degree_X_pow_le _).trans (WithBot.coe_le_coe.2 <| Nat.le_of_lt_succ <| Finset.mem_range.1 hk)
 set_option linter.uppercaseLean3 false in
-#align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLe_eq_span_X_pow
+#align polynomial.degree_le_eq_span_X_pow Polynomial.degreeLE_eq_span_X_pow
 
-theorem mem_degreeLt {n : ℕ} {f : R[X]} : f ∈ degreeLt R n ↔ degree f < n := by
-  rw [degreeLt, Submodule.mem_infᵢ]
+theorem mem_degreeLT {n : ℕ} {f : R[X]} : f ∈ degreeLT R n ↔ degree f < n := by
+  rw [degreeLT, Submodule.mem_infᵢ]
   conv_lhs => intro i; rw [Submodule.mem_infᵢ]
   rw [degree, Finset.max_eq_sup_coe]
   rw [Finset.sup_lt_iff ?_]
@@ -106,18 +106,18 @@ theorem mem_degreeLt {n : ℕ} {f : R[X]} : f ∈ degreeLt R n ↔ degree f < n
     simp only [mem_support_iff]
     intro b; rw [Nat.cast_withBot, WithBot.coe_lt_coe, lt_iff_not_le]
     change ¬ coeff f b = 0 → ¬ n ≤ b; rw [not_imp_not]
-#align polynomial.mem_degree_lt Polynomial.mem_degreeLt
+#align polynomial.mem_degree_lt Polynomial.mem_degreeLT
 
 @[mono]
-theorem degreeLt_mono {m n : ℕ} (H : m ≤ n) : degreeLt R m ≤ degreeLt R n := fun _ hf =>
-  mem_degreeLt.2 (lt_of_lt_of_le (mem_degreeLt.1 hf) <| WithBot.coe_le_coe.2 H)
-#align polynomial.degree_lt_mono Polynomial.degreeLt_mono
+theorem degreeLT_mono {m n : ℕ} (H : m ≤ n) : degreeLT R m ≤ degreeLT R n := fun _ hf =>
+  mem_degreeLT.2 (lt_of_lt_of_le (mem_degreeLT.1 hf) <| WithBot.coe_le_coe.2 H)
+#align polynomial.degree_lt_mono Polynomial.degreeLT_mono
 
-theorem degreeLt_eq_span_X_pow {n : ℕ} :
-    degreeLt R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) := by
+theorem degreeLT_eq_span_X_pow {n : ℕ} :
+    degreeLT R n = Submodule.span R ↑((Finset.range n).image fun n => X ^ n : Finset R[X]) := by
   apply le_antisymm
   · intro p hp
-    replace hp := mem_degreeLt.1 hp
+    replace hp := mem_degreeLT.1 hp
     rw [← Polynomial.sum_monomial_eq p, Polynomial.sum]
     refine' Submodule.sum_mem _ fun k hk => _
     show monomial _ _ ∈ _
@@ -128,18 +128,18 @@ theorem degreeLt_eq_span_X_pow {n : ℕ} :
         (Submodule.subset_span <|
           Finset.mem_coe.2 <| Finset.mem_image.2 ⟨_, Finset.mem_range.2 this, rfl⟩)
   rw [Submodule.span_le, Finset.coe_image, Set.image_subset_iff]
-  intro k hk; apply mem_degreeLt.2
+  intro k hk; apply mem_degreeLT.2
   exact lt_of_le_of_lt (degree_X_pow_le _) (WithBot.coe_lt_coe.2 <| Finset.mem_range.1 hk)
 set_option linter.uppercaseLean3 false in
-#align polynomial.degree_lt_eq_span_X_pow Polynomial.degreeLt_eq_span_X_pow
+#align polynomial.degree_lt_eq_span_X_pow Polynomial.degreeLT_eq_span_X_pow
 
-/-- The first `n` coefficients on `degree_lt n` form a linear equivalence with `fin n → R`. -/
-def degreeLtEquiv (R) [Semiring R] (n : ℕ) : degreeLt R n ≃ₗ[R] Fin n → R where
+/-- The first `n` coefficients on `degreeLT n` form a linear equivalence with `Fin n → R`. -/
+def degreeLTEquiv (R) [Semiring R] (n : ℕ) : degreeLT R n ≃ₗ[R] Fin n → R where
   toFun p n := (↑p : R[X]).coeff n
   invFun f :=
     ⟨∑ i : Fin n, monomial i (f i),
-      (degreeLt R n).sum_mem fun i _ =>
-        mem_degreeLt.mpr
+      (degreeLT R n).sum_mem fun i _ =>
+        mem_degreeLT.mpr
           (lt_of_le_of_lt (degree_monomial_le i (f i)) (WithBot.coe_lt_coe.mpr i.is_lt))⟩
   map_add' p q := by
     ext
@@ -156,7 +156,7 @@ def degreeLtEquiv (R) [Semiring R] (n : ℕ) : degreeLt R n ≃ₗ[R] Fin n →
     by_cases hp0 : p = 0
     · subst hp0
       simp only [coeff_zero, LinearMap.map_zero, Finset.sum_const_zero]
-    rw [mem_degreeLt, degree_eq_natDegree hp0,
+    rw [mem_degreeLT, degree_eq_natDegree hp0,
       Nat.cast_withBot, Nat.cast_withBot, WithBot.coe_lt_coe] at hp
     conv_rhs => rw [p.as_sum_range' n hp, ← Fin.sum_univ_eq_sum_range]
   right_inv := by
@@ -168,19 +168,19 @@ def degreeLtEquiv (R) [Semiring R] (n : ℕ) : degreeLt R n ≃ₗ[R] Fin n →
       rwa [← Fin.ext_iff]
     · intro h
       exact (h (Finset.mem_univ _)).elim
-#align polynomial.degree_lt_equiv Polynomial.degreeLtEquiv
+#align polynomial.degree_lt_equiv Polynomial.degreeLTEquiv
 
 -- Porting note: removed @[simp] as simp can prove this
-theorem degreeLtEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n) :
-    degreeLtEquiv _ _ ⟨p, hp⟩ = 0 ↔ p = 0 := by
+theorem degreeLTEquiv_eq_zero_iff_eq_zero {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) :
+    degreeLTEquiv _ _ ⟨p, hp⟩ = 0 ↔ p = 0 := by
   rw [LinearEquiv.map_eq_zero_iff, Submodule.mk_eq_zero]
-#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLtEquiv_eq_zero_iff_eq_zero
+#align polynomial.degree_lt_equiv_eq_zero_iff_eq_zero Polynomial.degreeLTEquiv_eq_zero_iff_eq_zero
 
-theorem eval_eq_sum_degreeLtEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLt R n) (x : R) :
-    p.eval x = ∑ i, degreeLtEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) := by
+theorem eval_eq_sum_degreeLTEquiv {n : ℕ} {p : R[X]} (hp : p ∈ degreeLT R n) (x : R) :
+    p.eval x = ∑ i, degreeLTEquiv _ _ ⟨p, hp⟩ i * x ^ (i : ℕ) := by
   simp_rw [eval_eq_sum]
-  exact (sum_fin _ (by simp_rw [MulZeroClass.zero_mul, forall_const]) (mem_degreeLt.mp hp)).symm
-#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLtEquiv
+  exact (sum_fin _ (by simp_rw [MulZeroClass.zero_mul, forall_const]) (mem_degreeLT.mp hp)).symm
+#align polynomial.eval_eq_sum_degree_lt_equiv Polynomial.eval_eq_sum_degreeLTEquiv
 
 /-- The finset of nonzero coefficients of a polynomial. -/
 def frange (p : R[X]) : Finset R :=
@@ -508,14 +508,14 @@ variable (I)
 
 /-- Given an ideal `I` of `R[X]`, make the `R`-submodule of `I`
 consisting of polynomials of degree ≤ `n`. -/
-def degreeLe (n : WithBot ℕ) : Submodule R R[X] :=
-  Polynomial.degreeLe R n ⊓ I.ofPolynomial
-#align ideal.degree_le Ideal.degreeLe
+def degreeLE (n : WithBot ℕ) : Submodule R R[X] :=
+  Polynomial.degreeLE R n ⊓ I.ofPolynomial
+#align ideal.degree_le Ideal.degreeLE
 
 /-- Given an ideal `I` of `R[X]`, make the ideal in `R` of
 leading coefficients of polynomials in `I` with degree ≤ `n`. -/
 def leadingCoeffNth (n : ℕ) : Ideal R :=
-  (I.degreeLe n).map <| lcoeff R n
+  (I.degreeLE n).map <| lcoeff R n
 #align ideal.leading_coeff_nth Ideal.leadingCoeffNth
 
 /-- Given an ideal `I` in `R[X]`, make the ideal in `R` of the
@@ -578,8 +578,8 @@ variable (I : Ideal R[X])
 
 theorem mem_leadingCoeffNth (n : ℕ) (x) :
     x ∈ I.leadingCoeffNth n ↔ ∃ p ∈ I, degree p ≤ n ∧ p.leadingCoeff = x := by
-  simp only [leadingCoeffNth, degreeLe, Submodule.mem_map, lcoeff_apply, Submodule.mem_inf,
-    mem_degreeLe]
+  simp only [leadingCoeffNth, degreeLE, Submodule.mem_map, lcoeff_apply, Submodule.mem_inf,
+    mem_degreeLE]
   constructor
   · rintro ⟨p, ⟨hpdeg, hpI⟩, rfl⟩
     cases' lt_or_eq_of_le hpdeg with hpdeg hpdeg
@@ -696,7 +696,7 @@ theorem isPrime_map_C_iff_isPrime (P : Ideal R) :
     IsPrime (map (C : R →+* R[X]) P : Ideal R[X]) ↔ IsPrime P := by
   -- Porting note: the following proof avoids quotient rings
   -- It can be golfed substantially by using something like
-  -- `(quotient.is_domain_iff_prime (map C P : ideal R[X]))`
+  -- `(Quotient.isDomain_iff_prime (map C P : Ideal R[X]))`
   constructor
   · intro H
     have := @comap_isPrime R R[X] (R →+* R[X]) _ _ _ C (map C P) H
@@ -756,12 +756,12 @@ theorem isPrime_map_C_of_isPrime {P : Ideal R} (H : IsPrime P) :
 set_option linter.uppercaseLean3 false in
 #align ideal.is_prime_map_C_of_is_prime Ideal.isPrime_map_C_of_isPrime
 
-theorem is_fg_degreeLe [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
-    Submodule.Fg (I.degreeLe n) :=
+theorem is_fg_degreeLE [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
+    Submodule.Fg (I.degreeLE n) :=
   isNoetherian_submodule_left.1
     -- porting note: times out without explicit `R`.
-    (isNoetherian_of_fg_of_noetherian _ ⟨_, (degreeLe_eq_span_X_pow (R := R)).symm⟩) _
-#align ideal.is_fg_degree_le Ideal.is_fg_degreeLe
+    (isNoetherian_of_fg_of_noetherian _ ⟨_, (degreeLE_eq_span_X_pow (R := R)).symm⟩) _
+#align ideal.is_fg_degree_le Ideal.is_fg_degreeLE
 
 end CommRing
 
@@ -918,7 +918,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
           (Set.range I.leadingCoeffNth) ⟨_, ⟨0, rfl⟩⟩
       have hm : M ∈ Set.range I.leadingCoeffNth := WellFounded.min_mem _ _ _
       let ⟨N, HN⟩ := hm
-      let ⟨s, hs⟩ := I.is_fg_degreeLe N
+      let ⟨s, hs⟩ := I.is_fg_degreeLE N
       have hm2 : ∀ k, I.leadingCoeffNth k ≤ M := fun k =>
         Or.casesOn (le_or_lt k N) (fun h => HN ▸ I.leadingCoeffNth_mono h) fun h x hx =>
           Classical.by_contradiction fun hxm =>
@@ -926,14 +926,14 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
             have : ¬M < I.leadingCoeffNth k := by
               refine' WellFounded.not_lt_min (wellFounded_submodule_gt R R) _ _ _ ; exact ⟨k, rfl⟩
             this ⟨HN ▸ I.leadingCoeffNth_mono (le_of_lt h), fun H => hxm (H hx)⟩
-      have hs2 : ∀ {x}, x ∈ I.degreeLe N → x ∈ Ideal.span (↑s : Set R[X]) :=
+      have hs2 : ∀ {x}, x ∈ I.degreeLE N → x ∈ Ideal.span (↑s : Set R[X]) :=
         hs ▸ fun hx =>
           Submodule.span_induction hx (fun _ hx => Ideal.subset_span hx) (Ideal.zero_mem _)
             (fun _ _ => Ideal.add_mem _) fun c f hf => f.C_mul' c ▸ Ideal.mul_mem_left _ _ hf
       ⟨s,
         le_antisymm
             (Ideal.span_le.2 fun x hx =>
-              have : x ∈ I.degreeLe N := hs ▸ Submodule.subset_span hx
+              have : x ∈ I.degreeLE N := hs ▸ Submodule.subset_span hx
               this.2) <|
           by
           have : Submodule.span R[X] ↑s = Ideal.span ↑s := by rfl
@@ -945,7 +945,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
           · subst k
             refine'
               hs2
-                ⟨Polynomial.mem_degreeLe.2
+                ⟨Polynomial.mem_degreeLE.2
                     (le_trans Polynomial.degree_le_natDegree <| WithBot.coe_le_coe.2 h),
                   hp⟩
           · have hp0 : p ≠ 0 := by
@@ -995,7 +995,7 @@ protected theorem Polynomial.isNoetherianRing [inst : IsNoetherianRing R] : IsNo
               refine' ih _ _ (I.sub_mem hp (I.mul_mem_right _ hq)) rfl
               rwa [Polynomial.degree_eq_natDegree hpq, Nat.cast_withBot, Nat.cast_withBot,
                 WithBot.coe_lt_coe, hn] at this
-            exact hs2 ⟨Polynomial.mem_degreeLe.2 hdq, hq⟩⟩⟩
+            exact hs2 ⟨Polynomial.mem_degreeLE.2 hdq, hq⟩⟩⟩
 #align polynomial.is_noetherian_ring Polynomial.isNoetherianRing
 
 attribute [instance] Polynomial.isNoetherianRing

This forward-ports changes from leanprover-community/mathlib#11364

One unrelated downstream file times out, presumably due to the import graph subtly changing.

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

@@ -759,7 +759,8 @@ set_option linter.uppercaseLean3 false in
 theorem is_fg_degreeLe [IsNoetherianRing R] (I : Ideal R[X]) (n : ℕ) :
     Submodule.Fg (I.degreeLe n) :=
   isNoetherian_submodule_left.1
-    (isNoetherian_of_fg_of_noetherian _ ⟨_, degreeLe_eq_span_X_pow.symm⟩) _
+    -- porting note: times out without explicit `R`.
+    (isNoetherian_of_fg_of_noetherian _ ⟨_, (degreeLe_eq_span_X_pow (R := R)).symm⟩) _
 #align ideal.is_fg_degree_le Ideal.is_fg_degreeLe
 
 end CommRing
@@ -1301,4 +1302,3 @@ instance (priority := 100) : UniqueFactorizationMonoid (MvPolynomial σ D) := by
 end MvPolynomial
 
 end UniqueFactorizationDomain
-

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