algebra.cubic_discriminant ⟷ Mathlib.Algebra.CubicDiscriminant

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

@@ -753,7 +753,7 @@ theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x,
   by
   rw [← _root_.map_ne_zero φ, disc_eq_prod_three_roots ha h3, pow_two]
   simp_rw [mul_ne_zero_iff, sub_ne_zero, _root_.map_ne_zero, and_self_iff, and_iff_right ha,
-    and_assoc']
+    and_assoc]
 #align cubic.disc_ne_zero_iff_roots_ne Cubic.disc_ne_zero_iff_roots_ne
 -/
 

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Kurniadi Angdinata
 -/
-import Data.Polynomial.Splits
+import Algebra.Polynomial.Splits
 
 #align_import algebra.cubic_discriminant from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Kurniadi Angdinata
 -/
-import Mathbin.Data.Polynomial.Splits
+import Data.Polynomial.Splits
 
 #align_import algebra.cubic_discriminant from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Kurniadi Angdinata
-
-! This file was ported from Lean 3 source module algebra.cubic_discriminant
-! 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.Data.Polynomial.Splits
 
+#align_import algebra.cubic_discriminant from "leanprover-community/mathlib"@"31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0"
+
 /-!
 # Cubics and discriminants
 

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

@@ -74,17 +74,21 @@ def toPoly (P : Cubic R) : R[X] :=
 #align cubic.to_poly Cubic.toPoly
 -/
 
+#print Cubic.C_mul_prod_X_sub_C_eq /-
 theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
     C w * (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨w, w * -(x + y + z), w * (x * y + x * z + y * z), w * -(x * y * z)⟩ :=
   by simp only [to_poly, C_neg, C_add, C_mul]; ring1
 #align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eq
+-/
 
+#print Cubic.prod_X_sub_C_eq /-
 theorem prod_X_sub_C_eq [CommRing S] {x y z : S} :
     (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨1, -(x + y + z), x * y + x * z + y * z, -(x * y * z)⟩ :=
   by rw [← one_mul <| X - C x, ← C_1, C_mul_prod_X_sub_C_eq, one_mul, one_mul, one_mul]
 #align cubic.prod_X_sub_C_eq Cubic.prod_X_sub_C_eq
+-/
 
 /-! ### Coefficients -/
 
@@ -103,10 +107,12 @@ private theorem coeffs :
   any_goals linarith only [hn]
   repeat' rw [zero_add]
 
+#print Cubic.coeff_eq_zero /-
 @[simp]
 theorem coeff_eq_zero {n : ℕ} (hn : 3 < n) : P.toPoly.coeff n = 0 :=
   coeffs.1 n hn
 #align cubic.coeff_eq_zero Cubic.coeff_eq_zero
+-/
 
 #print Cubic.coeff_eq_a /-
 @[simp]
@@ -162,103 +168,147 @@ theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
 #align cubic.to_poly_injective Cubic.toPoly_injective
 -/
 
+#print Cubic.of_a_eq_zero /-
 theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
   rw [to_poly, ha, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_a_eq_zero Cubic.of_a_eq_zero
+-/
 
+#print Cubic.of_a_eq_zero' /-
 theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
   of_a_eq_zero rfl
 #align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'
+-/
 
+#print Cubic.of_b_eq_zero /-
 theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.d := by
   rw [of_a_eq_zero ha, hb, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_b_eq_zero Cubic.of_b_eq_zero
+-/
 
+#print Cubic.of_b_eq_zero' /-
 theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
   of_b_eq_zero rfl rfl
 #align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'
+-/
 
+#print Cubic.of_c_eq_zero /-
 theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C P.d := by
   rw [of_b_eq_zero ha hb, hc, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_c_eq_zero Cubic.of_c_eq_zero
+-/
 
+#print Cubic.of_c_eq_zero' /-
 theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = C d :=
   of_c_eq_zero rfl rfl rfl
 #align cubic.of_c_eq_zero' Cubic.of_c_eq_zero'
+-/
 
+#print Cubic.of_d_eq_zero /-
 theorem of_d_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 0) : P.toPoly = 0 :=
   by rw [of_c_eq_zero ha hb hc, hd, C_0]
 #align cubic.of_d_eq_zero Cubic.of_d_eq_zero
+-/
 
+#print Cubic.of_d_eq_zero' /-
 theorem of_d_eq_zero' : (⟨0, 0, 0, 0⟩ : Cubic R).toPoly = 0 :=
   of_d_eq_zero rfl rfl rfl rfl
 #align cubic.of_d_eq_zero' Cubic.of_d_eq_zero'
+-/
 
+#print Cubic.zero /-
 theorem zero : (0 : Cubic R).toPoly = 0 :=
   of_d_eq_zero'
 #align cubic.zero Cubic.zero
+-/
 
+#print Cubic.toPoly_eq_zero_iff /-
 theorem toPoly_eq_zero_iff (P : Cubic R) : P.toPoly = 0 ↔ P = 0 := by rw [← zero, to_poly_injective]
 #align cubic.to_poly_eq_zero_iff Cubic.toPoly_eq_zero_iff
+-/
 
 private theorem ne_zero (h0 : P.a ≠ 0 ∨ P.b ≠ 0 ∨ P.c ≠ 0 ∨ P.d ≠ 0) : P.toPoly ≠ 0 := by
   contrapose! h0; rw [(to_poly_eq_zero_iff P).mp h0]; exact ⟨rfl, rfl, rfl, rfl⟩
 
+#print Cubic.ne_zero_of_a_ne_zero /-
 theorem ne_zero_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp NeZero).1 ha
 #align cubic.ne_zero_of_a_ne_zero Cubic.ne_zero_of_a_ne_zero
+-/
 
+#print Cubic.ne_zero_of_b_ne_zero /-
 theorem ne_zero_of_b_ne_zero (hb : P.b ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp NeZero).2).1 hb
 #align cubic.ne_zero_of_b_ne_zero Cubic.ne_zero_of_b_ne_zero
+-/
 
+#print Cubic.ne_zero_of_c_ne_zero /-
 theorem ne_zero_of_c_ne_zero (hc : P.c ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp (or_imp.mp NeZero).2).2).1 hc
 #align cubic.ne_zero_of_c_ne_zero Cubic.ne_zero_of_c_ne_zero
+-/
 
+#print Cubic.ne_zero_of_d_ne_zero /-
 theorem ne_zero_of_d_ne_zero (hd : P.d ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp (or_imp.mp NeZero).2).2).2 hd
 #align cubic.ne_zero_of_d_ne_zero Cubic.ne_zero_of_d_ne_zero
+-/
 
+#print Cubic.leadingCoeff_of_a_ne_zero /-
 @[simp]
 theorem leadingCoeff_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.leadingCoeff = P.a :=
   leadingCoeff_cubic ha
 #align cubic.leading_coeff_of_a_ne_zero Cubic.leadingCoeff_of_a_ne_zero
+-/
 
+#print Cubic.leadingCoeff_of_a_ne_zero' /-
 @[simp]
 theorem leadingCoeff_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).leadingCoeff = a :=
   leadingCoeff_of_a_ne_zero ha
 #align cubic.leading_coeff_of_a_ne_zero' Cubic.leadingCoeff_of_a_ne_zero'
+-/
 
+#print Cubic.leadingCoeff_of_b_ne_zero /-
 @[simp]
 theorem leadingCoeff_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.leadingCoeff = P.b := by
   rw [of_a_eq_zero ha, leading_coeff_quadratic hb]
 #align cubic.leading_coeff_of_b_ne_zero Cubic.leadingCoeff_of_b_ne_zero
+-/
 
+#print Cubic.leadingCoeff_of_b_ne_zero' /-
 @[simp]
 theorem leadingCoeff_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).leadingCoeff = b :=
   leadingCoeff_of_b_ne_zero rfl hb
 #align cubic.leading_coeff_of_b_ne_zero' Cubic.leadingCoeff_of_b_ne_zero'
+-/
 
+#print Cubic.leadingCoeff_of_c_ne_zero /-
 @[simp]
 theorem leadingCoeff_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) :
     P.toPoly.leadingCoeff = P.c := by rw [of_b_eq_zero ha hb, leading_coeff_linear hc]
 #align cubic.leading_coeff_of_c_ne_zero Cubic.leadingCoeff_of_c_ne_zero
+-/
 
+#print Cubic.leadingCoeff_of_c_ne_zero' /-
 @[simp]
 theorem leadingCoeff_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).leadingCoeff = c :=
   leadingCoeff_of_c_ne_zero rfl rfl hc
 #align cubic.leading_coeff_of_c_ne_zero' Cubic.leadingCoeff_of_c_ne_zero'
+-/
 
+#print Cubic.leadingCoeff_of_c_eq_zero /-
 @[simp]
 theorem leadingCoeff_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
     P.toPoly.leadingCoeff = P.d := by rw [of_c_eq_zero ha hb hc, leading_coeff_C]
 #align cubic.leading_coeff_of_c_eq_zero Cubic.leadingCoeff_of_c_eq_zero
+-/
 
+#print Cubic.leadingCoeff_of_c_eq_zero' /-
 @[simp]
 theorem leadingCoeff_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).leadingCoeff = d :=
   leadingCoeff_of_c_eq_zero rfl rfl rfl
 #align cubic.leading_coeff_of_c_eq_zero' Cubic.leadingCoeff_of_c_eq_zero'
+-/
 
 #print Cubic.monic_of_a_eq_one /-
 theorem monic_of_a_eq_one (ha : P.a = 1) : P.toPoly.Monic :=
@@ -274,29 +324,39 @@ theorem monic_of_a_eq_one' : (toPoly ⟨1, b, c, d⟩).Monic :=
 #align cubic.monic_of_a_eq_one' Cubic.monic_of_a_eq_one'
 -/
 
+#print Cubic.monic_of_b_eq_one /-
 theorem monic_of_b_eq_one (ha : P.a = 0) (hb : P.b = 1) : P.toPoly.Monic :=
   by
   nontriviality
   rw [monic, leading_coeff_of_b_ne_zero ha <| by rw [hb]; exact one_ne_zero, hb]
 #align cubic.monic_of_b_eq_one Cubic.monic_of_b_eq_one
+-/
 
+#print Cubic.monic_of_b_eq_one' /-
 theorem monic_of_b_eq_one' : (toPoly ⟨0, 1, c, d⟩).Monic :=
   monic_of_b_eq_one rfl rfl
 #align cubic.monic_of_b_eq_one' Cubic.monic_of_b_eq_one'
+-/
 
+#print Cubic.monic_of_c_eq_one /-
 theorem monic_of_c_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 1) : P.toPoly.Monic :=
   by
   nontriviality
   rw [monic, leading_coeff_of_c_ne_zero ha hb <| by rw [hc]; exact one_ne_zero, hc]
 #align cubic.monic_of_c_eq_one Cubic.monic_of_c_eq_one
+-/
 
+#print Cubic.monic_of_c_eq_one' /-
 theorem monic_of_c_eq_one' : (toPoly ⟨0, 0, 1, d⟩).Monic :=
   monic_of_c_eq_one rfl rfl rfl
 #align cubic.monic_of_c_eq_one' Cubic.monic_of_c_eq_one'
+-/
 
+#print Cubic.monic_of_d_eq_one /-
 theorem monic_of_d_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 1) :
     P.toPoly.Monic := by rw [monic, leading_coeff_of_c_eq_zero ha hb hc, hd]
 #align cubic.monic_of_d_eq_one Cubic.monic_of_d_eq_one
+-/
 
 #print Cubic.monic_of_d_eq_one' /-
 theorem monic_of_d_eq_one' : (toPoly ⟨0, 0, 0, 1⟩).Monic :=
@@ -327,145 +387,205 @@ def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
 #align cubic.equiv Cubic.equiv
 -/
 
+#print Cubic.degree_of_a_ne_zero /-
 @[simp]
 theorem degree_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.degree = 3 :=
   degree_cubic ha
 #align cubic.degree_of_a_ne_zero Cubic.degree_of_a_ne_zero
+-/
 
+#print Cubic.degree_of_a_ne_zero' /-
 @[simp]
 theorem degree_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).degree = 3 :=
   degree_of_a_ne_zero ha
 #align cubic.degree_of_a_ne_zero' Cubic.degree_of_a_ne_zero'
+-/
 
+#print Cubic.degree_of_a_eq_zero /-
 theorem degree_of_a_eq_zero (ha : P.a = 0) : P.toPoly.degree ≤ 2 := by
   simpa only [of_a_eq_zero ha] using degree_quadratic_le
 #align cubic.degree_of_a_eq_zero Cubic.degree_of_a_eq_zero
+-/
 
+#print Cubic.degree_of_a_eq_zero' /-
 theorem degree_of_a_eq_zero' : (toPoly ⟨0, b, c, d⟩).degree ≤ 2 :=
   degree_of_a_eq_zero rfl
 #align cubic.degree_of_a_eq_zero' Cubic.degree_of_a_eq_zero'
+-/
 
+#print Cubic.degree_of_b_ne_zero /-
 @[simp]
 theorem degree_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.degree = 2 := by
   rw [of_a_eq_zero ha, degree_quadratic hb]
 #align cubic.degree_of_b_ne_zero Cubic.degree_of_b_ne_zero
+-/
 
+#print Cubic.degree_of_b_ne_zero' /-
 @[simp]
 theorem degree_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).degree = 2 :=
   degree_of_b_ne_zero rfl hb
 #align cubic.degree_of_b_ne_zero' Cubic.degree_of_b_ne_zero'
+-/
 
+#print Cubic.degree_of_b_eq_zero /-
 theorem degree_of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly.degree ≤ 1 := by
   simpa only [of_b_eq_zero ha hb] using degree_linear_le
 #align cubic.degree_of_b_eq_zero Cubic.degree_of_b_eq_zero
+-/
 
+#print Cubic.degree_of_b_eq_zero' /-
 theorem degree_of_b_eq_zero' : (toPoly ⟨0, 0, c, d⟩).degree ≤ 1 :=
   degree_of_b_eq_zero rfl rfl
 #align cubic.degree_of_b_eq_zero' Cubic.degree_of_b_eq_zero'
+-/
 
+#print Cubic.degree_of_c_ne_zero /-
 @[simp]
 theorem degree_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) : P.toPoly.degree = 1 := by
   rw [of_b_eq_zero ha hb, degree_linear hc]
 #align cubic.degree_of_c_ne_zero Cubic.degree_of_c_ne_zero
+-/
 
+#print Cubic.degree_of_c_ne_zero' /-
 @[simp]
 theorem degree_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).degree = 1 :=
   degree_of_c_ne_zero rfl rfl hc
 #align cubic.degree_of_c_ne_zero' Cubic.degree_of_c_ne_zero'
+-/
 
+#print Cubic.degree_of_c_eq_zero /-
 theorem degree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly.degree ≤ 0 := by
   simpa only [of_c_eq_zero ha hb hc] using degree_C_le
 #align cubic.degree_of_c_eq_zero Cubic.degree_of_c_eq_zero
+-/
 
+#print Cubic.degree_of_c_eq_zero' /-
 theorem degree_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).degree ≤ 0 :=
   degree_of_c_eq_zero rfl rfl rfl
 #align cubic.degree_of_c_eq_zero' Cubic.degree_of_c_eq_zero'
+-/
 
+#print Cubic.degree_of_d_ne_zero /-
 @[simp]
 theorem degree_of_d_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d ≠ 0) :
     P.toPoly.degree = 0 := by rw [of_c_eq_zero ha hb hc, degree_C hd]
 #align cubic.degree_of_d_ne_zero Cubic.degree_of_d_ne_zero
+-/
 
+#print Cubic.degree_of_d_ne_zero' /-
 @[simp]
 theorem degree_of_d_ne_zero' (hd : d ≠ 0) : (toPoly ⟨0, 0, 0, d⟩).degree = 0 :=
   degree_of_d_ne_zero rfl rfl rfl hd
 #align cubic.degree_of_d_ne_zero' Cubic.degree_of_d_ne_zero'
+-/
 
+#print Cubic.degree_of_d_eq_zero /-
 @[simp]
 theorem degree_of_d_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 0) :
     P.toPoly.degree = ⊥ := by rw [of_d_eq_zero ha hb hc hd, degree_zero]
 #align cubic.degree_of_d_eq_zero Cubic.degree_of_d_eq_zero
+-/
 
+#print Cubic.degree_of_d_eq_zero' /-
 @[simp]
 theorem degree_of_d_eq_zero' : (⟨0, 0, 0, 0⟩ : Cubic R).toPoly.degree = ⊥ :=
   degree_of_d_eq_zero rfl rfl rfl rfl
 #align cubic.degree_of_d_eq_zero' Cubic.degree_of_d_eq_zero'
+-/
 
+#print Cubic.degree_of_zero /-
 @[simp]
 theorem degree_of_zero : (0 : Cubic R).toPoly.degree = ⊥ :=
   degree_of_d_eq_zero'
 #align cubic.degree_of_zero Cubic.degree_of_zero
+-/
 
+#print Cubic.natDegree_of_a_ne_zero /-
 @[simp]
 theorem natDegree_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.natDegree = 3 :=
   natDegree_cubic ha
 #align cubic.nat_degree_of_a_ne_zero Cubic.natDegree_of_a_ne_zero
+-/
 
+#print Cubic.natDegree_of_a_ne_zero' /-
 @[simp]
 theorem natDegree_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).natDegree = 3 :=
   natDegree_of_a_ne_zero ha
 #align cubic.nat_degree_of_a_ne_zero' Cubic.natDegree_of_a_ne_zero'
+-/
 
+#print Cubic.natDegree_of_a_eq_zero /-
 theorem natDegree_of_a_eq_zero (ha : P.a = 0) : P.toPoly.natDegree ≤ 2 := by
   simpa only [of_a_eq_zero ha] using nat_degree_quadratic_le
 #align cubic.nat_degree_of_a_eq_zero Cubic.natDegree_of_a_eq_zero
+-/
 
+#print Cubic.natDegree_of_a_eq_zero' /-
 theorem natDegree_of_a_eq_zero' : (toPoly ⟨0, b, c, d⟩).natDegree ≤ 2 :=
   natDegree_of_a_eq_zero rfl
 #align cubic.nat_degree_of_a_eq_zero' Cubic.natDegree_of_a_eq_zero'
+-/
 
+#print Cubic.natDegree_of_b_ne_zero /-
 @[simp]
 theorem natDegree_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.natDegree = 2 := by
   rw [of_a_eq_zero ha, nat_degree_quadratic hb]
 #align cubic.nat_degree_of_b_ne_zero Cubic.natDegree_of_b_ne_zero
+-/
 
+#print Cubic.natDegree_of_b_ne_zero' /-
 @[simp]
 theorem natDegree_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).natDegree = 2 :=
   natDegree_of_b_ne_zero rfl hb
 #align cubic.nat_degree_of_b_ne_zero' Cubic.natDegree_of_b_ne_zero'
+-/
 
+#print Cubic.natDegree_of_b_eq_zero /-
 theorem natDegree_of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly.natDegree ≤ 1 := by
   simpa only [of_b_eq_zero ha hb] using nat_degree_linear_le
 #align cubic.nat_degree_of_b_eq_zero Cubic.natDegree_of_b_eq_zero
+-/
 
+#print Cubic.natDegree_of_b_eq_zero' /-
 theorem natDegree_of_b_eq_zero' : (toPoly ⟨0, 0, c, d⟩).natDegree ≤ 1 :=
   natDegree_of_b_eq_zero rfl rfl
 #align cubic.nat_degree_of_b_eq_zero' Cubic.natDegree_of_b_eq_zero'
+-/
 
+#print Cubic.natDegree_of_c_ne_zero /-
 @[simp]
 theorem natDegree_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) :
     P.toPoly.natDegree = 1 := by rw [of_b_eq_zero ha hb, nat_degree_linear hc]
 #align cubic.nat_degree_of_c_ne_zero Cubic.natDegree_of_c_ne_zero
+-/
 
+#print Cubic.natDegree_of_c_ne_zero' /-
 @[simp]
 theorem natDegree_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).natDegree = 1 :=
   natDegree_of_c_ne_zero rfl rfl hc
 #align cubic.nat_degree_of_c_ne_zero' Cubic.natDegree_of_c_ne_zero'
+-/
 
+#print Cubic.natDegree_of_c_eq_zero /-
 @[simp]
 theorem natDegree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
     P.toPoly.natDegree = 0 := by rw [of_c_eq_zero ha hb hc, nat_degree_C]
 #align cubic.nat_degree_of_c_eq_zero Cubic.natDegree_of_c_eq_zero
+-/
 
+#print Cubic.natDegree_of_c_eq_zero' /-
 @[simp]
 theorem natDegree_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).natDegree = 0 :=
   natDegree_of_c_eq_zero rfl rfl rfl
 #align cubic.nat_degree_of_c_eq_zero' Cubic.natDegree_of_c_eq_zero'
+-/
 
+#print Cubic.natDegree_of_zero /-
 @[simp]
 theorem natDegree_of_zero : (0 : Cubic R).toPoly.natDegree = 0 :=
   natDegree_of_c_eq_zero'
 #align cubic.nat_degree_of_zero Cubic.natDegree_of_zero
+-/
 
 end Degree
 
@@ -517,12 +637,14 @@ theorem map_roots [IsDomain S] : (map φ P).roots = (Polynomial.map φ P.toPoly)
 #align cubic.map_roots Cubic.map_roots
 -/
 
+#print Cubic.mem_roots_iff /-
 theorem mem_roots_iff [IsDomain R] (h0 : P.toPoly ≠ 0) (x : R) :
     x ∈ P.roots ↔ P.a * x ^ 3 + P.b * x ^ 2 + P.c * x + P.d = 0 :=
   by
   rw [roots, mem_roots h0, is_root, to_poly]
   simp only [eval_C, eval_X, eval_add, eval_mul, eval_pow]
 #align cubic.mem_roots_iff Cubic.mem_roots_iff
+-/
 
 #print Cubic.card_roots_le /-
 theorem card_roots_le [IsDomain R] [DecidableEq R] : P.roots.toFinset.card ≤ 3 :=
@@ -543,6 +665,7 @@ variable {P : Cubic F} [Field F] [Field K] {φ : F →+* K} {x y z : K}
 
 section Split
 
+#print Cubic.splits_iff_card_roots /-
 theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ P).roots.card = 3 :=
   by
   replace ha : (map φ P).a ≠ 0 := (_root_.map_ne_zero φ).mpr ha
@@ -550,12 +673,16 @@ theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ
   rw [roots, ← splits_map_iff, ← map_to_poly, splits_iff_card_roots, ←
     ((degree_eq_iff_nat_degree_eq <| ne_zero_of_a_ne_zero ha).mp <| degree_of_a_ne_zero ha : _ = 3)]
 #align cubic.splits_iff_card_roots Cubic.splits_iff_card_roots
+-/
 
+#print Cubic.splits_iff_roots_eq_three /-
 theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
     Splits φ P.toPoly ↔ ∃ x y z : K, (map φ P).roots = {x, y, z} := by
   rw [splits_iff_card_roots ha, card_eq_three]
 #align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_three
+-/
 
+#print Cubic.eq_prod_three_roots /-
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
   by
@@ -566,7 +693,9 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
   change C (φ P.a) * ((X - C x) ::ₘ (X - C y) ::ₘ {X - C z}).Prod = _
   rw [prod_cons, prod_cons, prod_singleton, mul_assoc, mul_assoc]
 #align cubic.eq_prod_three_roots Cubic.eq_prod_three_roots
+-/
 
+#print Cubic.eq_sum_three_roots /-
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
       ⟨φ P.a, φ P.a * -(x + y + z), φ P.a * (x * y + x * z + y * z), φ P.a * -(x * y * z)⟩ :=
@@ -575,18 +704,25 @@ theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
   any_goals exact fun P Q => (to_poly_injective P Q).mp
   rw [eq_prod_three_roots ha h3, C_mul_prod_X_sub_C_eq]
 #align cubic.eq_sum_three_roots Cubic.eq_sum_three_roots
+-/
 
+#print Cubic.b_eq_three_roots /-
 theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.b = φ P.a * -(x + y + z) := by injection eq_sum_three_roots ha h3
 #align cubic.b_eq_three_roots Cubic.b_eq_three_roots
+-/
 
+#print Cubic.c_eq_three_roots /-
 theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.c = φ P.a * (x * y + x * z + y * z) := by injection eq_sum_three_roots ha h3
 #align cubic.c_eq_three_roots Cubic.c_eq_three_roots
+-/
 
+#print Cubic.d_eq_three_roots /-
 theorem d_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.d = φ P.a * -(x * y * z) := by injection eq_sum_three_roots ha h3
 #align cubic.d_eq_three_roots Cubic.d_eq_three_roots
+-/
 
 end Split
 
@@ -603,6 +739,7 @@ def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
 #align cubic.disc Cubic.disc
 -/
 
+#print Cubic.disc_eq_prod_three_roots /-
 theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.disc = (φ P.a * φ P.a * (x - y) * (x - z) * (y - z)) ^ 2 :=
   by
@@ -611,7 +748,9 @@ theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y
   rw [b_eq_three_roots ha h3, c_eq_three_roots ha h3, d_eq_three_roots ha h3]
   ring1
 #align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_roots
+-/
 
+#print Cubic.disc_ne_zero_iff_roots_ne /-
 theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ x ≠ y ∧ x ≠ z ∧ y ≠ z :=
   by
@@ -619,7 +758,9 @@ theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x,
   simp_rw [mul_ne_zero_iff, sub_ne_zero, _root_.map_ne_zero, and_self_iff, and_iff_right ha,
     and_assoc']
 #align cubic.disc_ne_zero_iff_roots_ne Cubic.disc_ne_zero_iff_roots_ne
+-/
 
+#print Cubic.disc_ne_zero_iff_roots_nodup /-
 theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ (map φ P).roots.Nodup :=
   by
@@ -629,7 +770,9 @@ theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {
   simp only [nodup_singleton]
   tauto
 #align cubic.disc_ne_zero_iff_roots_nodup Cubic.disc_ne_zero_iff_roots_nodup
+-/
 
+#print Cubic.card_roots_of_disc_ne_zero /-
 theorem card_roots_of_disc_ne_zero [DecidableEq K] (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
     (hd : P.disc ≠ 0) : (map φ P).roots.toFinset.card = 3 :=
   by
@@ -637,6 +780,7 @@ theorem card_roots_of_disc_ne_zero [DecidableEq K] (ha : P.a ≠ 0) (h3 : (map 
     splits_iff_card_roots ha, splits_iff_roots_eq_three ha]
   exact ⟨x, ⟨y, ⟨z, h3⟩⟩⟩
 #align cubic.card_roots_of_disc_ne_zero Cubic.card_roots_of_disc_ne_zero
+-/
 
 end Discriminant
 

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

@@ -53,7 +53,7 @@ namespace Cubic
 
 open Cubic Polynomial
 
-open Polynomial
+open scoped Polynomial
 
 variable {R S F K : Type _}
 
@@ -311,6 +311,7 @@ end Coeff
 
 section Degree
 
+#print Cubic.equiv /-
 /-- The equivalence between cubic polynomials and polynomials of degree at most three. -/
 @[simps]
 def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
@@ -324,6 +325,7 @@ def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
     rw [coeff_eq_zero h3,
       (degree_le_iff_coeff_zero (f : R[X]) 3).mp f.2 _ <| with_bot.coe_lt_coe.mpr h3]
 #align cubic.equiv Cubic.equiv
+-/
 
 @[simp]
 theorem degree_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.degree = 3 :=

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

@@ -74,18 +74,12 @@ def toPoly (P : Cubic R) : R[X] :=
 #align cubic.to_poly Cubic.toPoly
 -/
 
-/- warning: cubic.C_mul_prod_X_sub_C_eq -> Cubic.C_mul_prod_X_sub_C_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eqₓ'. -/
 theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
     C w * (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨w, w * -(x + y + z), w * (x * y + x * z + y * z), w * -(x * y * z)⟩ :=
   by simp only [to_poly, C_neg, C_add, C_mul]; ring1
 #align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eq
 
-/- warning: cubic.prod_X_sub_C_eq -> Cubic.prod_X_sub_C_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.prod_X_sub_C_eq Cubic.prod_X_sub_C_eqₓ'. -/
 theorem prod_X_sub_C_eq [CommRing S] {x y z : S} :
     (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨1, -(x + y + z), x * y + x * z + y * z, -(x * y * z)⟩ :=
@@ -109,12 +103,6 @@ private theorem coeffs :
   any_goals linarith only [hn]
   repeat' rw [zero_add]
 
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 @[simp]
 theorem coeff_eq_zero {n : ℕ} (hn : 3 < n) : P.toPoly.coeff n = 0 :=
   coeffs.1 n hn
@@ -174,225 +162,99 @@ theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
 #align cubic.to_poly_injective Cubic.toPoly_injective
 -/
 
-/- warning: cubic.of_a_eq_zero -> Cubic.of_a_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero Cubic.of_a_eq_zeroₓ'. -/
 theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
   rw [to_poly, ha, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_a_eq_zero Cubic.of_a_eq_zero
 
-/- warning: cubic.of_a_eq_zero' -> Cubic.of_a_eq_zero' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'ₓ'. -/
 theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
   of_a_eq_zero rfl
 #align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'
 
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 theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.d := by
   rw [of_a_eq_zero ha, hb, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_b_eq_zero Cubic.of_b_eq_zero
 
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 theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
   of_b_eq_zero rfl rfl
 #align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'
 
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 theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C P.d := by
   rw [of_b_eq_zero ha hb, hc, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_c_eq_zero Cubic.of_c_eq_zero
 
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 theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = C d :=
   of_c_eq_zero rfl rfl rfl
 #align cubic.of_c_eq_zero' Cubic.of_c_eq_zero'
 
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 theorem of_d_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 0) : P.toPoly = 0 :=
   by rw [of_c_eq_zero ha hb hc, hd, C_0]
 #align cubic.of_d_eq_zero Cubic.of_d_eq_zero
 
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 theorem of_d_eq_zero' : (⟨0, 0, 0, 0⟩ : Cubic R).toPoly = 0 :=
   of_d_eq_zero rfl rfl rfl rfl
 #align cubic.of_d_eq_zero' Cubic.of_d_eq_zero'
 
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 theorem zero : (0 : Cubic R).toPoly = 0 :=
   of_d_eq_zero'
 #align cubic.zero Cubic.zero
 
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 theorem toPoly_eq_zero_iff (P : Cubic R) : P.toPoly = 0 ↔ P = 0 := by rw [← zero, to_poly_injective]
 #align cubic.to_poly_eq_zero_iff Cubic.toPoly_eq_zero_iff
 
 private theorem ne_zero (h0 : P.a ≠ 0 ∨ P.b ≠ 0 ∨ P.c ≠ 0 ∨ P.d ≠ 0) : P.toPoly ≠ 0 := by
   contrapose! h0; rw [(to_poly_eq_zero_iff P).mp h0]; exact ⟨rfl, rfl, rfl, rfl⟩
 
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 theorem ne_zero_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp NeZero).1 ha
 #align cubic.ne_zero_of_a_ne_zero Cubic.ne_zero_of_a_ne_zero
 
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 theorem ne_zero_of_b_ne_zero (hb : P.b ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp NeZero).2).1 hb
 #align cubic.ne_zero_of_b_ne_zero Cubic.ne_zero_of_b_ne_zero
 
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 theorem ne_zero_of_c_ne_zero (hc : P.c ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp (or_imp.mp NeZero).2).2).1 hc
 #align cubic.ne_zero_of_c_ne_zero Cubic.ne_zero_of_c_ne_zero
 
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 theorem ne_zero_of_d_ne_zero (hd : P.d ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp (or_imp.mp NeZero).2).2).2 hd
 #align cubic.ne_zero_of_d_ne_zero Cubic.ne_zero_of_d_ne_zero
 
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 @[simp]
 theorem leadingCoeff_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.leadingCoeff = P.a :=
   leadingCoeff_cubic ha
 #align cubic.leading_coeff_of_a_ne_zero Cubic.leadingCoeff_of_a_ne_zero
 
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 @[simp]
 theorem leadingCoeff_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).leadingCoeff = a :=
   leadingCoeff_of_a_ne_zero ha
 #align cubic.leading_coeff_of_a_ne_zero' Cubic.leadingCoeff_of_a_ne_zero'
 
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 @[simp]
 theorem leadingCoeff_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.leadingCoeff = P.b := by
   rw [of_a_eq_zero ha, leading_coeff_quadratic hb]
 #align cubic.leading_coeff_of_b_ne_zero Cubic.leadingCoeff_of_b_ne_zero
 
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 @[simp]
 theorem leadingCoeff_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).leadingCoeff = b :=
   leadingCoeff_of_b_ne_zero rfl hb
 #align cubic.leading_coeff_of_b_ne_zero' Cubic.leadingCoeff_of_b_ne_zero'
 
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 @[simp]
 theorem leadingCoeff_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) :
     P.toPoly.leadingCoeff = P.c := by rw [of_b_eq_zero ha hb, leading_coeff_linear hc]
 #align cubic.leading_coeff_of_c_ne_zero Cubic.leadingCoeff_of_c_ne_zero
 
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 @[simp]
 theorem leadingCoeff_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).leadingCoeff = c :=
   leadingCoeff_of_c_ne_zero rfl rfl hc
 #align cubic.leading_coeff_of_c_ne_zero' Cubic.leadingCoeff_of_c_ne_zero'
 
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 @[simp]
 theorem leadingCoeff_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
     P.toPoly.leadingCoeff = P.d := by rw [of_c_eq_zero ha hb hc, leading_coeff_C]
 #align cubic.leading_coeff_of_c_eq_zero Cubic.leadingCoeff_of_c_eq_zero
 
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 @[simp]
 theorem leadingCoeff_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).leadingCoeff = d :=
   leadingCoeff_of_c_eq_zero rfl rfl rfl
@@ -412,56 +274,26 @@ theorem monic_of_a_eq_one' : (toPoly ⟨1, b, c, d⟩).Monic :=
 #align cubic.monic_of_a_eq_one' Cubic.monic_of_a_eq_one'
 -/
 
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 theorem monic_of_b_eq_one (ha : P.a = 0) (hb : P.b = 1) : P.toPoly.Monic :=
   by
   nontriviality
   rw [monic, leading_coeff_of_b_ne_zero ha <| by rw [hb]; exact one_ne_zero, hb]
 #align cubic.monic_of_b_eq_one Cubic.monic_of_b_eq_one
 
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 theorem monic_of_b_eq_one' : (toPoly ⟨0, 1, c, d⟩).Monic :=
   monic_of_b_eq_one rfl rfl
 #align cubic.monic_of_b_eq_one' Cubic.monic_of_b_eq_one'
 
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 theorem monic_of_c_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 1) : P.toPoly.Monic :=
   by
   nontriviality
   rw [monic, leading_coeff_of_c_ne_zero ha hb <| by rw [hc]; exact one_ne_zero, hc]
 #align cubic.monic_of_c_eq_one Cubic.monic_of_c_eq_one
 
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 theorem monic_of_c_eq_one' : (toPoly ⟨0, 0, 1, d⟩).Monic :=
   monic_of_c_eq_one rfl rfl rfl
 #align cubic.monic_of_c_eq_one' Cubic.monic_of_c_eq_one'
 
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 theorem monic_of_d_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 1) :
     P.toPoly.Monic := by rw [monic, leading_coeff_of_c_eq_zero ha hb hc, hd]
 #align cubic.monic_of_d_eq_one Cubic.monic_of_d_eq_one
@@ -479,12 +311,6 @@ end Coeff
 
 section Degree
 
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 /-- The equivalence between cubic polynomials and polynomials of degree at most three. -/
 @[simps]
 def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
@@ -499,321 +325,141 @@ def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
       (degree_le_iff_coeff_zero (f : R[X]) 3).mp f.2 _ <| with_bot.coe_lt_coe.mpr h3]
 #align cubic.equiv Cubic.equiv
 
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 @[simp]
 theorem degree_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.degree = 3 :=
   degree_cubic ha
 #align cubic.degree_of_a_ne_zero Cubic.degree_of_a_ne_zero
 
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 @[simp]
 theorem degree_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).degree = 3 :=
   degree_of_a_ne_zero ha
 #align cubic.degree_of_a_ne_zero' Cubic.degree_of_a_ne_zero'
 
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 theorem degree_of_a_eq_zero (ha : P.a = 0) : P.toPoly.degree ≤ 2 := by
   simpa only [of_a_eq_zero ha] using degree_quadratic_le
 #align cubic.degree_of_a_eq_zero Cubic.degree_of_a_eq_zero
 
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 theorem degree_of_a_eq_zero' : (toPoly ⟨0, b, c, d⟩).degree ≤ 2 :=
   degree_of_a_eq_zero rfl
 #align cubic.degree_of_a_eq_zero' Cubic.degree_of_a_eq_zero'
 
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 @[simp]
 theorem degree_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.degree = 2 := by
   rw [of_a_eq_zero ha, degree_quadratic hb]
 #align cubic.degree_of_b_ne_zero Cubic.degree_of_b_ne_zero
 
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 @[simp]
 theorem degree_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).degree = 2 :=
   degree_of_b_ne_zero rfl hb
 #align cubic.degree_of_b_ne_zero' Cubic.degree_of_b_ne_zero'
 
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 theorem degree_of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly.degree ≤ 1 := by
   simpa only [of_b_eq_zero ha hb] using degree_linear_le
 #align cubic.degree_of_b_eq_zero Cubic.degree_of_b_eq_zero
 
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 theorem degree_of_b_eq_zero' : (toPoly ⟨0, 0, c, d⟩).degree ≤ 1 :=
   degree_of_b_eq_zero rfl rfl
 #align cubic.degree_of_b_eq_zero' Cubic.degree_of_b_eq_zero'
 
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 @[simp]
 theorem degree_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) : P.toPoly.degree = 1 := by
   rw [of_b_eq_zero ha hb, degree_linear hc]
 #align cubic.degree_of_c_ne_zero Cubic.degree_of_c_ne_zero
 
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 @[simp]
 theorem degree_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).degree = 1 :=
   degree_of_c_ne_zero rfl rfl hc
 #align cubic.degree_of_c_ne_zero' Cubic.degree_of_c_ne_zero'
 
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 theorem degree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly.degree ≤ 0 := by
   simpa only [of_c_eq_zero ha hb hc] using degree_C_le
 #align cubic.degree_of_c_eq_zero Cubic.degree_of_c_eq_zero
 
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 theorem degree_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).degree ≤ 0 :=
   degree_of_c_eq_zero rfl rfl rfl
 #align cubic.degree_of_c_eq_zero' Cubic.degree_of_c_eq_zero'
 
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 @[simp]
 theorem degree_of_d_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d ≠ 0) :
     P.toPoly.degree = 0 := by rw [of_c_eq_zero ha hb hc, degree_C hd]
 #align cubic.degree_of_d_ne_zero Cubic.degree_of_d_ne_zero
 
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 @[simp]
 theorem degree_of_d_ne_zero' (hd : d ≠ 0) : (toPoly ⟨0, 0, 0, d⟩).degree = 0 :=
   degree_of_d_ne_zero rfl rfl rfl hd
 #align cubic.degree_of_d_ne_zero' Cubic.degree_of_d_ne_zero'
 
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 @[simp]
 theorem degree_of_d_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 0) :
     P.toPoly.degree = ⊥ := by rw [of_d_eq_zero ha hb hc hd, degree_zero]
 #align cubic.degree_of_d_eq_zero Cubic.degree_of_d_eq_zero
 
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 @[simp]
 theorem degree_of_d_eq_zero' : (⟨0, 0, 0, 0⟩ : Cubic R).toPoly.degree = ⊥ :=
   degree_of_d_eq_zero rfl rfl rfl rfl
 #align cubic.degree_of_d_eq_zero' Cubic.degree_of_d_eq_zero'
 
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 @[simp]
 theorem degree_of_zero : (0 : Cubic R).toPoly.degree = ⊥ :=
   degree_of_d_eq_zero'
 #align cubic.degree_of_zero Cubic.degree_of_zero
 
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 @[simp]
 theorem natDegree_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.natDegree = 3 :=
   natDegree_cubic ha
 #align cubic.nat_degree_of_a_ne_zero Cubic.natDegree_of_a_ne_zero
 
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 @[simp]
 theorem natDegree_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).natDegree = 3 :=
   natDegree_of_a_ne_zero ha
 #align cubic.nat_degree_of_a_ne_zero' Cubic.natDegree_of_a_ne_zero'
 
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 theorem natDegree_of_a_eq_zero (ha : P.a = 0) : P.toPoly.natDegree ≤ 2 := by
   simpa only [of_a_eq_zero ha] using nat_degree_quadratic_le
 #align cubic.nat_degree_of_a_eq_zero Cubic.natDegree_of_a_eq_zero
 
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 theorem natDegree_of_a_eq_zero' : (toPoly ⟨0, b, c, d⟩).natDegree ≤ 2 :=
   natDegree_of_a_eq_zero rfl
 #align cubic.nat_degree_of_a_eq_zero' Cubic.natDegree_of_a_eq_zero'
 
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 @[simp]
 theorem natDegree_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.natDegree = 2 := by
   rw [of_a_eq_zero ha, nat_degree_quadratic hb]
 #align cubic.nat_degree_of_b_ne_zero Cubic.natDegree_of_b_ne_zero
 
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 @[simp]
 theorem natDegree_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).natDegree = 2 :=
   natDegree_of_b_ne_zero rfl hb
 #align cubic.nat_degree_of_b_ne_zero' Cubic.natDegree_of_b_ne_zero'
 
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 theorem natDegree_of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly.natDegree ≤ 1 := by
   simpa only [of_b_eq_zero ha hb] using nat_degree_linear_le
 #align cubic.nat_degree_of_b_eq_zero Cubic.natDegree_of_b_eq_zero
 
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 theorem natDegree_of_b_eq_zero' : (toPoly ⟨0, 0, c, d⟩).natDegree ≤ 1 :=
   natDegree_of_b_eq_zero rfl rfl
 #align cubic.nat_degree_of_b_eq_zero' Cubic.natDegree_of_b_eq_zero'
 
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 @[simp]
 theorem natDegree_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) :
     P.toPoly.natDegree = 1 := by rw [of_b_eq_zero ha hb, nat_degree_linear hc]
 #align cubic.nat_degree_of_c_ne_zero Cubic.natDegree_of_c_ne_zero
 
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 @[simp]
 theorem natDegree_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).natDegree = 1 :=
   natDegree_of_c_ne_zero rfl rfl hc
 #align cubic.nat_degree_of_c_ne_zero' Cubic.natDegree_of_c_ne_zero'
 
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 @[simp]
 theorem natDegree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
     P.toPoly.natDegree = 0 := by rw [of_c_eq_zero ha hb hc, nat_degree_C]
 #align cubic.nat_degree_of_c_eq_zero Cubic.natDegree_of_c_eq_zero
 
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 @[simp]
 theorem natDegree_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).natDegree = 0 :=
   natDegree_of_c_eq_zero rfl rfl rfl
 #align cubic.nat_degree_of_c_eq_zero' Cubic.natDegree_of_c_eq_zero'
 
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 @[simp]
 theorem natDegree_of_zero : (0 : Cubic R).toPoly.natDegree = 0 :=
   natDegree_of_c_eq_zero'
@@ -869,12 +515,6 @@ theorem map_roots [IsDomain S] : (map φ P).roots = (Polynomial.map φ P.toPoly)
 #align cubic.map_roots Cubic.map_roots
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cubic.mem_roots_iff Cubic.mem_roots_iffₓ'. -/
 theorem mem_roots_iff [IsDomain R] (h0 : P.toPoly ≠ 0) (x : R) :
     x ∈ P.roots ↔ P.a * x ^ 3 + P.b * x ^ 2 + P.c * x + P.d = 0 :=
   by
@@ -901,12 +541,6 @@ variable {P : Cubic F} [Field F] [Field K] {φ : F →+* K} {x y z : K}
 
 section Split
 
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(AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K 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-Case conversion may be inaccurate. Consider using '#align cubic.splits_iff_card_roots Cubic.splits_iff_card_rootsₓ'. -/
 theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ P).roots.card = 3 :=
   by
   replace ha : (map φ P).a ≠ 0 := (_root_.map_ne_zero φ).mpr ha
@@ -915,20 +549,11 @@ theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ
     ((degree_eq_iff_nat_degree_eq <| ne_zero_of_a_ne_zero ha).mp <| degree_of_a_ne_zero ha : _ = 3)]
 #align cubic.splits_iff_card_roots Cubic.splits_iff_card_roots
 
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 theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
     Splits φ P.toPoly ↔ ∃ x y z : K, (map φ P).roots = {x, y, z} := by
   rw [splits_iff_card_roots ha, card_eq_three]
 #align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_three
 
-/- warning: cubic.eq_prod_three_roots -> Cubic.eq_prod_three_roots is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.eq_prod_three_roots Cubic.eq_prod_three_rootsₓ'. -/
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
   by
@@ -940,9 +565,6 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
   rw [prod_cons, prod_cons, prod_singleton, mul_assoc, mul_assoc]
 #align cubic.eq_prod_three_roots Cubic.eq_prod_three_roots
 
-/- warning: cubic.eq_sum_three_roots -> Cubic.eq_sum_three_roots is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.eq_sum_three_roots Cubic.eq_sum_three_rootsₓ'. -/
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
       ⟨φ P.a, φ P.a * -(x + y + z), φ P.a * (x * y + x * z + y * z), φ P.a * -(x * y * z)⟩ :=
@@ -952,23 +574,14 @@ theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
   rw [eq_prod_three_roots ha h3, C_mul_prod_X_sub_C_eq]
 #align cubic.eq_sum_three_roots Cubic.eq_sum_three_roots
 
-/- warning: cubic.b_eq_three_roots -> Cubic.b_eq_three_roots is a dubious translation:
-<too large>
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 theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.b = φ P.a * -(x + y + z) := by injection eq_sum_three_roots ha h3
 #align cubic.b_eq_three_roots Cubic.b_eq_three_roots
 
-/- warning: cubic.c_eq_three_roots -> Cubic.c_eq_three_roots is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.c_eq_three_roots Cubic.c_eq_three_rootsₓ'. -/
 theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.c = φ P.a * (x * y + x * z + y * z) := by injection eq_sum_three_roots ha h3
 #align cubic.c_eq_three_roots Cubic.c_eq_three_roots
 
-/- warning: cubic.d_eq_three_roots -> Cubic.d_eq_three_roots is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align cubic.d_eq_three_roots Cubic.d_eq_three_rootsₓ'. -/
 theorem d_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.d = φ P.a * -(x * y * z) := by injection eq_sum_three_roots ha h3
 #align cubic.d_eq_three_roots Cubic.d_eq_three_roots
@@ -988,9 +601,6 @@ def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
 #align cubic.disc Cubic.disc
 -/
 
-/- warning: cubic.disc_eq_prod_three_roots -> Cubic.disc_eq_prod_three_roots is a dubious translation:
-<too large>
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 theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.disc = (φ P.a * φ P.a * (x - y) * (x - z) * (y - z)) ^ 2 :=
   by
@@ -1000,12 +610,6 @@ theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y
   ring1
 #align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_roots
 
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 theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ x ≠ y ∧ x ≠ z ∧ y ≠ z :=
   by
@@ -1014,12 +618,6 @@ theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x,
     and_assoc']
 #align cubic.disc_ne_zero_iff_roots_ne Cubic.disc_ne_zero_iff_roots_ne
 
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 theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ (map φ P).roots.Nodup :=
   by
@@ -1030,12 +628,6 @@ theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {
   tauto
 #align cubic.disc_ne_zero_iff_roots_nodup Cubic.disc_ne_zero_iff_roots_nodup
 
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-Case conversion may be inaccurate. Consider using '#align cubic.card_roots_of_disc_ne_zero Cubic.card_roots_of_disc_ne_zeroₓ'. -/
 theorem card_roots_of_disc_ne_zero [DecidableEq K] (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
     (hd : P.disc ≠ 0) : (map φ P).roots.toFinset.card = 3 :=
   by

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

@@ -80,9 +80,7 @@ Case conversion may be inaccurate. Consider using '#align cubic.C_mul_prod_X_sub
 theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
     C w * (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨w, w * -(x + y + z), w * (x * y + x * z + y * z), w * -(x * y * z)⟩ :=
-  by
-  simp only [to_poly, C_neg, C_add, C_mul]
-  ring1
+  by simp only [to_poly, C_neg, C_add, C_mul]; ring1
 #align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eq
 
 /- warning: cubic.prod_X_sub_C_eq -> Cubic.prod_X_sub_C_eq is a dubious translation:
@@ -269,11 +267,8 @@ Case conversion may be inaccurate. Consider using '#align cubic.to_poly_eq_zero_
 theorem toPoly_eq_zero_iff (P : Cubic R) : P.toPoly = 0 ↔ P = 0 := by rw [← zero, to_poly_injective]
 #align cubic.to_poly_eq_zero_iff Cubic.toPoly_eq_zero_iff
 
-private theorem ne_zero (h0 : P.a ≠ 0 ∨ P.b ≠ 0 ∨ P.c ≠ 0 ∨ P.d ≠ 0) : P.toPoly ≠ 0 :=
-  by
-  contrapose! h0
-  rw [(to_poly_eq_zero_iff P).mp h0]
-  exact ⟨rfl, rfl, rfl, rfl⟩
+private theorem ne_zero (h0 : P.a ≠ 0 ∨ P.b ≠ 0 ∨ P.c ≠ 0 ∨ P.d ≠ 0) : P.toPoly ≠ 0 := by
+  contrapose! h0; rw [(to_poly_eq_zero_iff P).mp h0]; exact ⟨rfl, rfl, rfl, rfl⟩
 
 /- warning: cubic.ne_zero_of_a_ne_zero -> Cubic.ne_zero_of_a_ne_zero is a dubious translation:
 lean 3 declaration is
@@ -407,11 +402,7 @@ theorem leadingCoeff_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).leadingCoeff = d
 theorem monic_of_a_eq_one (ha : P.a = 1) : P.toPoly.Monic :=
   by
   nontriviality
-  rw [monic,
-    leading_coeff_of_a_ne_zero <| by
-      rw [ha]
-      exact one_ne_zero,
-    ha]
+  rw [monic, leading_coeff_of_a_ne_zero <| by rw [ha]; exact one_ne_zero, ha]
 #align cubic.monic_of_a_eq_one Cubic.monic_of_a_eq_one
 -/
 
@@ -430,11 +421,7 @@ Case conversion may be inaccurate. Consider using '#align cubic.monic_of_b_eq_on
 theorem monic_of_b_eq_one (ha : P.a = 0) (hb : P.b = 1) : P.toPoly.Monic :=
   by
   nontriviality
-  rw [monic,
-    leading_coeff_of_b_ne_zero ha <| by
-      rw [hb]
-      exact one_ne_zero,
-    hb]
+  rw [monic, leading_coeff_of_b_ne_zero ha <| by rw [hb]; exact one_ne_zero, hb]
 #align cubic.monic_of_b_eq_one Cubic.monic_of_b_eq_one
 
 /- warning: cubic.monic_of_b_eq_one' -> Cubic.monic_of_b_eq_one' is a dubious translation:
@@ -456,11 +443,7 @@ Case conversion may be inaccurate. Consider using '#align cubic.monic_of_c_eq_on
 theorem monic_of_c_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 1) : P.toPoly.Monic :=
   by
   nontriviality
-  rw [monic,
-    leading_coeff_of_c_ne_zero ha hb <| by
-      rw [hc]
-      exact one_ne_zero,
-    hc]
+  rw [monic, leading_coeff_of_c_ne_zero ha hb <| by rw [hc]; exact one_ne_zero, hc]
 #align cubic.monic_of_c_eq_one Cubic.monic_of_c_eq_one
 
 /- warning: cubic.monic_of_c_eq_one' -> Cubic.monic_of_c_eq_one' is a dubious translation:
@@ -904,12 +887,7 @@ theorem card_roots_le [IsDomain R] [DecidableEq R] : P.roots.toFinset.card ≤ 3
   by
   apply (to_finset_card_le P.to_poly.roots).trans
   by_cases hP : P.to_poly = 0
-  ·
-    exact
-      (card_roots' P.to_poly).trans
-        (by
-          rw [hP, nat_degree_zero]
-          exact zero_le 3)
+  · exact (card_roots' P.to_poly).trans (by rw [hP, nat_degree_zero]; exact zero_le 3)
   · exact WithBot.coe_le_coe.1 ((card_roots hP).trans degree_cubic_le)
 #align cubic.card_roots_le Cubic.card_roots_le
 -/

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

@@ -75,10 +75,7 @@ def toPoly (P : Cubic R) : R[X] :=
 -/
 
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(Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S 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(instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S 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(NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eqₓ'. -/
 theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
     C w * (X - C x) * (X - C y) * (X - C z) =
@@ -89,10 +86,7 @@ theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
 #align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eq
 
 /- warning: cubic.prod_X_sub_C_eq -> Cubic.prod_X_sub_C_eq is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.prod_X_sub_C_eq Cubic.prod_X_sub_C_eqₓ'. -/
 theorem prod_X_sub_C_eq [CommRing S] {x y z : S} :
     (X - C x) * (X - C y) * (X - C z) =
@@ -116,7 +110,6 @@ private theorem coeffs :
   repeat' rw [if_neg]
   any_goals linarith only [hn]
   repeat' rw [zero_add]
-#align cubic.coeffs cubic.coeffs
 
 /- warning: cubic.coeff_eq_zero -> Cubic.coeff_eq_zero is a dubious translation:
 lean 3 declaration is
@@ -184,20 +177,14 @@ theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
 -/
 
 /- warning: cubic.of_a_eq_zero -> Cubic.of_a_eq_zero is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero Cubic.of_a_eq_zeroₓ'. -/
 theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
   rw [to_poly, ha, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_a_eq_zero Cubic.of_a_eq_zero
 
 /- warning: cubic.of_a_eq_zero' -> Cubic.of_a_eq_zero' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'ₓ'. -/
 theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
   of_a_eq_zero rfl
@@ -287,7 +274,6 @@ private theorem ne_zero (h0 : P.a ≠ 0 ∨ P.b ≠ 0 ∨ P.c ≠ 0 ∨ P.d ≠
   contrapose! h0
   rw [(to_poly_eq_zero_iff P).mp h0]
   exact ⟨rfl, rfl, rfl, rfl⟩
-#align cubic.ne_zero cubic.ne_zero
 
 /- warning: cubic.ne_zero_of_a_ne_zero -> Cubic.ne_zero_of_a_ne_zero is a dubious translation:
 lean 3 declaration is
@@ -963,10 +949,7 @@ theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
 #align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_three
 
 /- warning: cubic.eq_prod_three_roots -> Cubic.eq_prod_three_roots is a dubious translation:
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(Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) 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(Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => 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(Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F 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(Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (HMul.hMul.{u1, u1, u1} ((fun 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(DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.eq_prod_three_roots Cubic.eq_prod_three_rootsₓ'. -/
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
@@ -980,10 +963,7 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 #align cubic.eq_prod_three_roots Cubic.eq_prod_three_roots
 
 /- warning: cubic.eq_sum_three_roots -> Cubic.eq_sum_three_roots is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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(Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.eq_sum_three_roots Cubic.eq_sum_three_rootsₓ'. -/
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
@@ -995,30 +975,21 @@ theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 #align cubic.eq_sum_three_roots Cubic.eq_sum_three_roots
 
 /- warning: cubic.b_eq_three_roots -> Cubic.b_eq_three_roots is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align cubic.b_eq_three_roots Cubic.b_eq_three_rootsₓ'. -/
 theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.b = φ P.a * -(x + y + z) := by injection eq_sum_three_roots ha h3
 #align cubic.b_eq_three_roots Cubic.b_eq_three_roots
 
 /- warning: cubic.c_eq_three_roots -> Cubic.c_eq_three_roots is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align cubic.c_eq_three_roots Cubic.c_eq_three_rootsₓ'. -/
 theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.c = φ P.a * (x * y + x * z + y * z) := by injection eq_sum_three_roots ha h3
 #align cubic.c_eq_three_roots Cubic.c_eq_three_roots
 
 /- warning: cubic.d_eq_three_roots -> Cubic.d_eq_three_roots is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.d_eq_three_roots Cubic.d_eq_three_rootsₓ'. -/
 theorem d_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.d = φ P.a * -(x * y * z) := by injection eq_sum_three_roots ha h3
@@ -1040,10 +1011,7 @@ def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
 -/
 
 /- warning: cubic.disc_eq_prod_three_roots -> Cubic.disc_eq_prod_three_roots is a dubious translation:
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=> K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x y)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x z)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) y z)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_rootsₓ'. -/
 theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.disc = (φ P.a * φ P.a * (x - y) * (x - z) * (y - z)) ^ 2 :=

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

@@ -78,7 +78,7 @@ def toPoly (P : Cubic R) : R[X] :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {w : S} {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S 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(CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Cubic.mk.{u1} S w (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z)))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {w : S} {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Cubic.mk.{u1} S w (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z)))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {w : S} {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Cubic.mk.{u1} S w (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z)))))
 Case conversion may be inaccurate. Consider using '#align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eqₓ'. -/
 theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
     C w * (X - C x) * (X - C y) * (X - C z) =
@@ -92,7 +92,7 @@ theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Cubic.mk.{u1} S (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y z)) (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Cubic.mk.{u1} S (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z)) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S 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(CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Cubic.mk.{u1} S (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z)) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.prod_X_sub_C_eq Cubic.prod_X_sub_C_eqₓ'. -/
 theorem prod_X_sub_C_eq [CommRing S] {x y z : S} :
     (X - C x) * (X - C y) * (X - C z) =
@@ -187,7 +187,7 @@ theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
 lean 3 declaration is
   forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Cubic.b.{u1} R P)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.X.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P))))
 but is expected to have type
-  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.d.{u1} R P)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.b.{u1} R P)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.X.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P))))
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.d.{u1} R P)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.b.{u1} R P)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.b.{u1} R P)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.X.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P))))
 Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero Cubic.of_a_eq_zeroₓ'. -/
 theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
   rw [to_poly, ha, C_0, MulZeroClass.zero_mul, zero_add]
@@ -197,7 +197,7 @@ theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P
 lean 3 declaration is
   forall {R : Type.{u1}} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) b c d)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) b) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) c) (Polynomial.X.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) d))
 but is expected to have type
-  forall {R : Type.{u1}} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) b c d)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) d) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) c) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) b) (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 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(Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) c) (Polynomial.X.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) d))
+  forall {R : Type.{u1}} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) b c d)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) d) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) b) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) b) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) c) (Polynomial.X.{u1} R _inst_1))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) d))
 Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'ₓ'. -/
 theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
   of_a_eq_zero rfl
@@ -207,7 +207,7 @@ theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
 lean 3 declaration is
   forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.X.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P))))
 but is expected to have type
-  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.d.{u1} R P)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P))))
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.d.{u1} R P)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.c.{u1} R P)) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P))))
 Case conversion may be inaccurate. Consider using '#align cubic.of_b_eq_zero Cubic.of_b_eq_zeroₓ'. -/
 theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.d := by
   rw [of_a_eq_zero ha, hb, C_0, MulZeroClass.zero_mul, zero_add]
@@ -217,7 +217,7 @@ theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.
 lean 3 declaration is
   forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) c d)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) c) (Polynomial.X.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) d))
 but is expected to have type
-  forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) c d)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) c) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) d) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) c) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) c) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) d))
+  forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) c d)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) d) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) c) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) c) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) d))
 Case conversion may be inaccurate. Consider using '#align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'ₓ'. -/
 theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
   of_b_eq_zero rfl rfl
@@ -227,7 +227,7 @@ theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
 lean 3 declaration is
   forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P)))
 but is expected to have type
-  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P)))
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 P) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Cubic.d.{u1} R P)))
 Case conversion may be inaccurate. Consider using '#align cubic.of_c_eq_zero Cubic.of_c_eq_zeroₓ'. -/
 theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C P.d := by
   rw [of_b_eq_zero ha hb, hc, C_0, MulZeroClass.zero_mul, zero_add]
@@ -237,7 +237,7 @@ theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C
 lean 3 declaration is
   forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) (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))))))) d)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) d)
 but is expected to have type
-  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) d)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) d)
+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) d)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) d)
 Case conversion may be inaccurate. Consider using '#align cubic.of_c_eq_zero' Cubic.of_c_eq_zero'ₓ'. -/
 theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = C d :=
   of_c_eq_zero rfl rfl rfl
@@ -966,7 +966,7 @@ theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Cubic.toPoly.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) x))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) y))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Cubic.toPoly.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => 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(Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (HMul.hMul.{u1, u1, u1} ((fun 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(DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Cubic.toPoly.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun 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(DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun 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(DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun 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(Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.eq_prod_three_roots Cubic.eq_prod_three_rootsₓ'. -/
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
@@ -983,7 +983,7 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} (Cubic.{u2} K) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P) (Cubic.mk.{u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x z)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) y z))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z)))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Cubic.{u1} K) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P) (Cubic.mk.{u1} K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F 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(HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Cubic.{u1} K) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P) (Cubic.mk.{u1} K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
 Case conversion may be inaccurate. Consider using '#align cubic.eq_sum_three_roots Cubic.eq_sum_three_rootsₓ'. -/
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
@@ -998,7 +998,7 @@ theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.b.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.b.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.b.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.b.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.b.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.b_eq_three_roots Cubic.b_eq_three_rootsₓ'. -/
 theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.b = φ P.a * -(x + y + z) := by injection eq_sum_three_roots ha h3
@@ -1008,7 +1008,7 @@ theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.c.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x z)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) y z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.c.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.c.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.c.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.c.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))))
 Case conversion may be inaccurate. Consider using '#align cubic.c_eq_three_roots Cubic.c_eq_three_rootsₓ'. -/
 theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.c = φ P.a * (x * y + x * z + y * z) := by injection eq_sum_three_roots ha h3
@@ -1018,7 +1018,7 @@ theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.d.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.d.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.d.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.d.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.d.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.d_eq_three_roots Cubic.d_eq_three_rootsₓ'. -/
 theorem d_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.d = φ P.a * -(x * y * z) := by injection eq_sum_three_roots ha h3
@@ -1043,7 +1043,7 @@ def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P)) (HPow.hPow.{u2, 0, u2} K Nat K (instHPow.{u2, 0} K Nat (Monoid.Pow.{u2} K (Ring.toMonoid.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P))) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) x y)) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) x z)) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) y z)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x y)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x z)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) y z)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x y)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x z)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) y z)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_rootsₓ'. -/
 theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.disc = (φ P.a * φ P.a * (x - y) * (x - z) * (y - z)) ^ 2 :=

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

@@ -510,7 +510,12 @@ end Coeff
 
 section Degree
 
-#print Cubic.equiv /-
+/- warning: cubic.equiv -> Cubic.equiv is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Equiv.{succ u1, succ u1} (Cubic.{u1} R) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (p : Polynomial.{u1} R _inst_1) => 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 p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 3 (OfNat.mk.{0} (WithBot.{0} Nat) 3 (bit1.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne) (WithBot.hasAdd.{0} Nat Nat.hasAdd) (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Equiv.{succ u1, succ u1} (Cubic.{u1} R) (Subtype.{succ u1} (Polynomial.{u1} R _inst_1) (fun (p : Polynomial.{u1} R _inst_1) => 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 p) (OfNat.ofNat.{0} (WithBot.{0} Nat) 3 (instOfNat.{0} (WithBot.{0} Nat) 3 (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)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align cubic.equiv Cubic.equivₓ'. -/
 /-- The equivalence between cubic polynomials and polynomials of degree at most three. -/
 @[simps]
 def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
@@ -524,7 +529,6 @@ def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
     rw [coeff_eq_zero h3,
       (degree_le_iff_coeff_zero (f : R[X]) 3).mp f.2 _ <| with_bot.coe_lt_coe.mpr h3]
 #align cubic.equiv Cubic.equiv
--/
 
 /- warning: cubic.degree_of_a_ne_zero -> Cubic.degree_of_a_ne_zero is a dubious translation:
 lean 3 declaration is
@@ -550,7 +554,7 @@ theorem degree_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).degree =
 
 /- warning: cubic.degree_of_a_eq_zero -> Cubic.degree_of_a_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (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)))))))) -> (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 _inst_1 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 2 (OfNat.mk.{0} (WithBot.{0} Nat) 2 (bit0.{0} (WithBot.{0} Nat) (WithBot.hasAdd.{0} Nat Nat.hasAdd) (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne))))))
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (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)))))))) -> (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 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 2 (OfNat.mk.{0} (WithBot.{0} Nat) 2 (bit0.{0} (WithBot.{0} Nat) (WithBot.hasAdd.{0} Nat Nat.hasAdd) (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne))))))
 but is expected to have type
   forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (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 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 2 (instOfNat.{0} (WithBot.{0} Nat) 2 (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)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align cubic.degree_of_a_eq_zero Cubic.degree_of_a_eq_zeroₓ'. -/
@@ -560,7 +564,7 @@ theorem degree_of_a_eq_zero (ha : P.a = 0) : P.toPoly.degree ≤ 2 := by
 
 /- warning: cubic.degree_of_a_eq_zero' -> Cubic.degree_of_a_eq_zero' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], 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 _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) b c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 2 (OfNat.mk.{0} (WithBot.{0} Nat) 2 (bit0.{0} (WithBot.{0} Nat) (WithBot.hasAdd.{0} Nat Nat.hasAdd) (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne)))))
+  forall {R : Type.{u1}} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], 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 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) b c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 2 (OfNat.mk.{0} (WithBot.{0} Nat) 2 (bit0.{0} (WithBot.{0} Nat) (WithBot.hasAdd.{0} Nat Nat.hasAdd) (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne)))))
 but is expected to have type
   forall {R : Type.{u1}} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], 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 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) b c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 2 (instOfNat.{0} (WithBot.{0} Nat) 2 (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)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align cubic.degree_of_a_eq_zero' Cubic.degree_of_a_eq_zero'ₓ'. -/
@@ -592,7 +596,7 @@ theorem degree_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).degree =
 
 /- warning: cubic.degree_of_b_eq_zero -> Cubic.degree_of_b_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (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)))))))) -> (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 _inst_1 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (OfNat.mk.{0} (WithBot.{0} Nat) 1 (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne)))))
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (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)))))))) -> (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 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (OfNat.mk.{0} (WithBot.{0} Nat) 1 (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne)))))
 but is expected to have type
   forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (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 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))
 Case conversion may be inaccurate. Consider using '#align cubic.degree_of_b_eq_zero Cubic.degree_of_b_eq_zeroₓ'. -/
@@ -602,7 +606,7 @@ theorem degree_of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly.degree ≤
 
 /- warning: cubic.degree_of_b_eq_zero' -> Cubic.degree_of_b_eq_zero' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], 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 _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (OfNat.mk.{0} (WithBot.{0} Nat) 1 (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne))))
+  forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], 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 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (OfNat.mk.{0} (WithBot.{0} Nat) 1 (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne))))
 but is expected to have type
   forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], 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 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 1 (One.toOfNat1.{0} (WithBot.{0} Nat) (WithBot.one.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))
 Case conversion may be inaccurate. Consider using '#align cubic.degree_of_b_eq_zero' Cubic.degree_of_b_eq_zero'ₓ'. -/
@@ -634,7 +638,7 @@ theorem degree_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).degree =
 
 /- warning: cubic.degree_of_c_eq_zero -> Cubic.degree_of_c_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (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)))))))) -> (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 _inst_1 (Cubic.toPoly.{u1} R _inst_1 P)) (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)))))
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (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)))))))) -> (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 (Cubic.toPoly.{u1} R _inst_1 P)) (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)))))
 but is expected to have type
   forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (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 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)))))
 Case conversion may be inaccurate. Consider using '#align cubic.degree_of_c_eq_zero Cubic.degree_of_c_eq_zeroₓ'. -/
@@ -644,7 +648,7 @@ theorem degree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toP
 
 /- warning: cubic.degree_of_c_eq_zero' -> Cubic.degree_of_c_eq_zero' is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], 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 _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) (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))))))) d))) (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))))
+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], 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 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) (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))))))) d))) (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))))
 but is expected to have type
   forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], 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 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 0 (Zero.toOfNat0.{0} (WithBot.{0} Nat) (WithBot.zero.{0} Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))))
 Case conversion may be inaccurate. Consider using '#align cubic.degree_of_c_eq_zero' Cubic.degree_of_c_eq_zero'ₓ'. -/

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

@@ -937,7 +937,7 @@ section Split
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Iff (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) P)) (Eq.{1} Nat (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} K) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} K) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} K) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} K) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} K) (Multiset.orderedCancelAddCommMonoid.{u2} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} K) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} K) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} K) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} K) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} K) (Multiset.orderedCancelAddCommMonoid.{u2} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} K) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} K) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} K) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} K) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} K) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} K) (Multiset.orderedCancelAddCommMonoid.{u2} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) 3 (instOfNatNat 3))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) 3 (instOfNatNat 3))))
 Case conversion may be inaccurate. Consider using '#align cubic.splits_iff_card_roots Cubic.splits_iff_card_rootsₓ'. -/
 theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ P).roots.card = 3 :=
   by
@@ -951,7 +951,7 @@ theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Iff (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) P)) (Exists.{succ u2} K (fun (x : K) => Exists.{succ u2} K (fun (y : K) => Exists.{succ u2} K (fun (z : K) => Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z))))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Exists.{succ u1} K (fun (x : K) => Exists.{succ u1} K (fun (y : K) => Exists.{succ u1} K (fun (z : K) => Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z))))))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Exists.{succ u1} K (fun (x : K) => Exists.{succ u1} K (fun (y : K) => Exists.{succ u1} K (fun (z : K) => Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z))))))))
 Case conversion may be inaccurate. Consider using '#align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_threeₓ'. -/
 theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
     Splits φ P.toPoly ↔ ∃ x y z : K, (map φ P).roots = {x, y, z} := by
@@ -962,7 +962,7 @@ theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Cubic.toPoly.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) x))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) y))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Cubic.toPoly.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F 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(Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 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(Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun 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K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K 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(Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Cubic.toPoly.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K 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(Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 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(DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) 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(DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => (fun 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K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.eq_prod_three_roots Cubic.eq_prod_three_rootsₓ'. -/
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
@@ -979,7 +979,7 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} (Cubic.{u2} K) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P) (Cubic.mk.{u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x z)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) y z))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z)))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Cubic.{u1} K) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P) (Cubic.mk.{u1} K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Cubic.{u1} K) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P) (Cubic.mk.{u1} K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
 Case conversion may be inaccurate. Consider using '#align cubic.eq_sum_three_roots Cubic.eq_sum_three_rootsₓ'. -/
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
@@ -994,7 +994,7 @@ theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.b.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.b.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.b.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.b.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.b.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.b_eq_three_roots Cubic.b_eq_three_rootsₓ'. -/
 theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.b = φ P.a * -(x + y + z) := by injection eq_sum_three_roots ha h3
@@ -1004,7 +1004,7 @@ theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.c.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x z)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) y z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.c.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.c.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.c.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.c.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))))
 Case conversion may be inaccurate. Consider using '#align cubic.c_eq_three_roots Cubic.c_eq_three_rootsₓ'. -/
 theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.c = φ P.a * (x * y + x * z + y * z) := by injection eq_sum_three_roots ha h3
@@ -1014,7 +1014,7 @@ theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.d.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.d.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.d.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.d.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.d.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.d_eq_three_roots Cubic.d_eq_three_rootsₓ'. -/
 theorem d_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.d = φ P.a * -(x * y * z) := by injection eq_sum_three_roots ha h3
@@ -1039,7 +1039,7 @@ def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P)) (HPow.hPow.{u2, 0, u2} K Nat K (instHPow.{u2, 0} K Nat (Monoid.Pow.{u2} K (Ring.toMonoid.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P))) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) x y)) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) x z)) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) y z)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x y)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x z)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) y z)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x y)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x z)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) y z)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_rootsₓ'. -/
 theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.disc = (φ P.a * φ P.a * (x - y) * (x - z) * (y - z)) ^ 2 :=
@@ -1054,7 +1054,7 @@ theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Iff (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (And (Ne.{succ u2} K x y) (And (Ne.{succ u2} K x z) (Ne.{succ u2} K y z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (And (Ne.{succ u1} K x y) (And (Ne.{succ u1} K x z) (Ne.{succ u1} K y z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (And (Ne.{succ u1} K x y) (And (Ne.{succ u1} K x z) (Ne.{succ u1} K y z))))
 Case conversion may be inaccurate. Consider using '#align cubic.disc_ne_zero_iff_roots_ne Cubic.disc_ne_zero_iff_roots_neₓ'. -/
 theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ x ≠ y ∧ x ≠ z ∧ y ≠ z :=
@@ -1068,7 +1068,7 @@ theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x,
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Iff (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (Multiset.Nodup.{u2} K (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Multiset.Nodup.{u1} K (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Multiset.Nodup.{u1} K (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Field.isDomain.{u1} K _inst_2) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))))
 Case conversion may be inaccurate. Consider using '#align cubic.disc_ne_zero_iff_roots_nodup Cubic.disc_ne_zero_iff_roots_nodupₓ'. -/
 theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ (map φ P).roots.Nodup :=
@@ -1084,7 +1084,7 @@ theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.instSingletonMultiset.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))
+  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.instSingletonMultiset.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))
 Case conversion may be inaccurate. Consider using '#align cubic.card_roots_of_disc_ne_zero Cubic.card_roots_of_disc_ne_zeroₓ'. -/
 theorem card_roots_of_disc_ne_zero [DecidableEq K] (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
     (hd : P.disc ≠ 0) : (map φ P).roots.toFinset.card = 3 :=

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

@@ -78,7 +78,7 @@ def toPoly (P : Cubic R) : R[X] :=
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {w : S} {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Cubic.mk.{u1} S w (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z)))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {w : S} {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Cubic.mk.{u1} S w (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z)))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {w : S} {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} 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S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Cubic.mk.{u1} S w (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z)))))
 Case conversion may be inaccurate. Consider using '#align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eqₓ'. -/
 theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
     C w * (X - C x) * (X - C y) * (X - C z) =
@@ -92,7 +92,7 @@ theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
 lean 3 declaration is
   forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Cubic.mk.{u1} S (OfNat.ofNat.{u1} S 1 (OfNat.mk.{u1} S 1 (One.one.{u1} S (AddMonoidWithOne.toOne.{u1} S (AddGroupWithOne.toAddMonoidWithOne.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y z)) (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z))))
 but is expected to have type
-  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) 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_inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) 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(Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S 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(Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Cubic.mk.{u1} S (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (NonAssocRing.toOne.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z)) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z))))
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) x)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z) (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2)) (Cubic.mk.{u1} S (OfNat.ofNat.{u1} S 1 (One.toOfNat1.{u1} S (Semiring.toOne.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_2))))) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) x y) z)) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) y z)) (Neg.neg.{u1} S (Ring.toNeg.{u1} S (CommRing.toRing.{u1} S _inst_2)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.prod_X_sub_C_eq Cubic.prod_X_sub_C_eqₓ'. -/
 theorem prod_X_sub_C_eq [CommRing S] {x y z : S} :
     (X - C x) * (X - C y) * (X - C z) =
@@ -900,7 +900,7 @@ theorem map_roots [IsDomain S] : (map φ P).roots = (Polynomial.map φ P.toPoly)
 lean 3 declaration is
   forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : CommRing.{u1} R] [_inst_3 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Cubic.toPoly.{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))))))) -> (forall (x : R), Iff (Membership.Mem.{u1, u1} R (Multiset.{u1} R) (Multiset.hasMem.{u1} R) x (Cubic.roots.{u1} R _inst_1 _inst_3 P)) (Eq.{succ u1} R (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toHasAdd.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Cubic.a.{u1} R P) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Cubic.b.{u1} R P) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Cubic.c.{u1} R P) x)) (Cubic.d.{u1} R P)) (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 (CommRing.toRing.{u1} R _inst_1)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : CommRing.{u1} R] [_inst_3 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], (Ne.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Cubic.toPoly.{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 (x : R), Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Cubic.roots.{u1} R _inst_1 _inst_3 P)) (Eq.{succ u1} R (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Cubic.a.{u1} R P) (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 (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Cubic.b.{u1} R P) (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 (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Cubic.c.{u1} R P) x)) (Cubic.d.{u1} R P)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3)))))))
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : CommRing.{u1} R] [_inst_3 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], (Ne.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Cubic.toPoly.{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 (x : R), Iff (Membership.mem.{u1, u1} R (Multiset.{u1} R) (Multiset.instMembershipMultiset.{u1} R) x (Cubic.roots.{u1} R _inst_1 _inst_3 P)) (Eq.{succ u1} R (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (Distrib.toAdd.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Cubic.a.{u1} R P) (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Cubic.b.{u1} R P) (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 (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Cubic.c.{u1} R P) x)) (Cubic.d.{u1} R P)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CancelCommMonoidWithZero.toCommMonoidWithZero.{u1} R (IsDomain.toCancelCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align cubic.mem_roots_iff Cubic.mem_roots_iffₓ'. -/
 theorem mem_roots_iff [IsDomain R] (h0 : P.toPoly ≠ 0) (x : R) :
     x ∈ P.roots ↔ P.a * x ^ 3 + P.b * x ^ 2 + P.c * x + P.d = 0 :=
@@ -937,7 +937,7 @@ section Split
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Iff (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) P)) (Eq.{1} Nat (coeFn.{succ u2, succ u2} (AddMonoidHom.{u2, 0} (Multiset.{u2} K) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} K) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} K) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} K) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} K) (Multiset.orderedCancelAddCommMonoid.{u2} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (fun (_x : AddMonoidHom.{u2, 0} (Multiset.{u2} K) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} K) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} K) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} K) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} K) (Multiset.orderedCancelAddCommMonoid.{u2} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) => (Multiset.{u2} K) -> Nat) (AddMonoidHom.hasCoeToFun.{u2, 0} (Multiset.{u2} K) Nat (AddMonoid.toAddZeroClass.{u2} (Multiset.{u2} K) (AddRightCancelMonoid.toAddMonoid.{u2} (Multiset.{u2} K) (AddCancelMonoid.toAddRightCancelMonoid.{u2} (Multiset.{u2} K) (AddCancelCommMonoid.toAddCancelMonoid.{u2} (Multiset.{u2} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u2} (Multiset.{u2} K) (Multiset.orderedCancelAddCommMonoid.{u2} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.card.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) 3 (instOfNatNat 3))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (FunLike.coe.{succ u1, succ u1, 1} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) (fun (_x : Multiset.{u1} K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) _x) (AddHomClass.toFunLike.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddZeroClass.toAdd.{u1} (Multiset.{u1} K) (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K))))))) (AddZeroClass.toAdd.{0} Nat (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (AddMonoidHomClass.toAddHomClass.{u1, u1, 0} (AddMonoidHom.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)) (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid) (AddMonoidHom.addMonoidHomClass.{u1, 0} (Multiset.{u1} K) Nat (AddMonoid.toAddZeroClass.{u1} (Multiset.{u1} K) (AddRightCancelMonoid.toAddMonoid.{u1} (Multiset.{u1} K) (AddCancelMonoid.toAddRightCancelMonoid.{u1} (Multiset.{u1} K) (AddCancelCommMonoid.toAddCancelMonoid.{u1} (Multiset.{u1} K) (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{u1} (Multiset.{u1} K) (Multiset.instOrderedCancelAddCommMonoidMultiset.{u1} K)))))) (AddMonoid.toAddZeroClass.{0} Nat Nat.addMonoid)))) (Multiset.card.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) 3 (instOfNatNat 3))))
 Case conversion may be inaccurate. Consider using '#align cubic.splits_iff_card_roots Cubic.splits_iff_card_rootsₓ'. -/
 theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ P).roots.card = 3 :=
   by
@@ -951,7 +951,7 @@ theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Iff (Polynomial.Splits.{u1, u2} F K (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u1} F (Ring.toSemiring.{u1} F (CommRing.toRing.{u1} F (EuclideanDomain.toCommRing.{u1} F (Field.toEuclideanDomain.{u1} F _inst_1)))) P)) (Exists.{succ u2} K (fun (x : K) => Exists.{succ u2} K (fun (y : K) => Exists.{succ u2} K (fun (z : K) => Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z))))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Exists.{succ u1} K (fun (x : K) => Exists.{succ u1} K (fun (y : K) => Exists.{succ u1} K (fun (z : K) => Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z))))))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Iff (Polynomial.Splits.{u2, u1} F K (EuclideanDomain.toCommRing.{u2} F (Field.toEuclideanDomain.{u2} F _inst_1)) _inst_2 φ (Cubic.toPoly.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) P)) (Exists.{succ u1} K (fun (x : K) => Exists.{succ u1} K (fun (y : K) => Exists.{succ u1} K (fun (z : K) => Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z))))))))
 Case conversion may be inaccurate. Consider using '#align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_threeₓ'. -/
 theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
     Splits φ P.toPoly ↔ ∃ x y z : K, (map φ P).roots = {x, y, z} := by
@@ -962,7 +962,7 @@ theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Cubic.toPoly.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHMul.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.mul'.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} 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(Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) x))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K 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(Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) y))) (HSub.hSub.{u2, u2, u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (instHSub.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.sub.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.X.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (coeFn.{succ u2, succ u2} (RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Cubic.toPoly.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) 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(NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) 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F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K 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K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Cubic.toPoly.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun 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(Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun 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(DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F 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(Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun 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(Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun 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K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun 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(Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))))) (Polynomial.C.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z) (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (instHSub.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.sub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (Polynomial.X.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (fun (_x : K) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : K) => Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K 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(Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.eq_prod_three_roots Cubic.eq_prod_three_rootsₓ'. -/
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
@@ -979,7 +979,7 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} (Cubic.{u2} K) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P) (Cubic.mk.{u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K 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K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K 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(NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z)))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Cubic.{u1} K) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P) (Cubic.mk.{u1} K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Cubic.{u1} K) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P) (Cubic.mk.{u1} K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
 Case conversion may be inaccurate. Consider using '#align cubic.eq_sum_three_roots Cubic.eq_sum_three_rootsₓ'. -/
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
@@ -994,7 +994,7 @@ theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.b.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.b.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.b.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.b.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.b.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.b_eq_three_roots Cubic.b_eq_three_rootsₓ'. -/
 theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.b = φ P.a * -(x + y + z) := by injection eq_sum_three_roots ha h3
@@ -1004,7 +1004,7 @@ theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.c.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x z)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) y z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.c.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.c.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.c.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.c.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))))
 Case conversion may be inaccurate. Consider using '#align cubic.c_eq_three_roots Cubic.c_eq_three_rootsₓ'. -/
 theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.c = φ P.a * (x * y + x * z + y * z) := by injection eq_sum_three_roots ha h3
@@ -1014,7 +1014,7 @@ theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.d.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.d.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.d.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.d.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.d.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z))))
 Case conversion may be inaccurate. Consider using '#align cubic.d_eq_three_roots Cubic.d_eq_three_rootsₓ'. -/
 theorem d_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.d = φ P.a * -(x * y * z) := by injection eq_sum_three_roots ha h3
@@ -1039,7 +1039,7 @@ def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P)) (HPow.hPow.{u2, 0, u2} K Nat K (instHPow.{u2, 0} K Nat (Monoid.Pow.{u2} K (Ring.toMonoid.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P))) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) x y)) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) x z)) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) y z)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) 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(DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x y)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x z)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) y z)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x y)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) x z)) (HSub.hSub.{u1, u1, u1} K K K (instHSub.{u1} K (Ring.toSub.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) y z)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_rootsₓ'. -/
 theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.disc = (φ P.a * φ P.a * (x - y) * (x - z) * (y - z)) ^ 2 :=
@@ -1054,7 +1054,7 @@ theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Iff (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (And (Ne.{succ u2} K x y) (And (Ne.{succ u2} K x z) (Ne.{succ u2} K y z))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (And (Ne.{succ u1} K x y) (And (Ne.{succ u1} K x z) (Ne.{succ u1} K y z))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (And (Ne.{succ u1} K x y) (And (Ne.{succ u1} K x z) (Ne.{succ u1} K y z))))
 Case conversion may be inaccurate. Consider using '#align cubic.disc_ne_zero_iff_roots_ne Cubic.disc_ne_zero_iff_roots_neₓ'. -/
 theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ x ≠ y ∧ x ≠ z ∧ y ≠ z :=
@@ -1068,7 +1068,7 @@ theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x,
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Iff (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) (Multiset.Nodup.{u2} K (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P))))
 but is expected to have type
-  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Multiset.Nodup.{u1} K (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))))
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (Semiring.toNonAssocSemiring.{u2} F (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Iff (Ne.{succ u2} F (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) (Multiset.Nodup.{u1} K (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))))
 Case conversion may be inaccurate. Consider using '#align cubic.disc_ne_zero_iff_roots_nodup Cubic.disc_ne_zero_iff_roots_nodupₓ'. -/
 theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ (map φ P).roots.Nodup :=
@@ -1084,7 +1084,7 @@ theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {
 lean 3 declaration is
   forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.instSingletonMultiset.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))
+  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (Semiring.toNonAssocSemiring.{u1} F (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1)))) (Semiring.toNonAssocSemiring.{u2} K (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.instSingletonMultiset.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToCommSemiringToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))
 Case conversion may be inaccurate. Consider using '#align cubic.card_roots_of_disc_ne_zero Cubic.card_roots_of_disc_ne_zeroₓ'. -/
 theorem card_roots_of_disc_ne_zero [DecidableEq K] (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
     (hd : P.disc ≠ 0) : (map φ P).roots.toFinset.card = 3 :=

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: David Kurniadi Angdinata
 
 ! This file was ported from Lean 3 source module algebra.cubic_discriminant
-! leanprover-community/mathlib commit 930133160e24036d5242039fe4972407cd4f1222
+! leanprover-community/mathlib commit 31ca6f9cf5f90a6206092cd7f84b359dcb6d52e0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Data.Polynomial.Splits
 /-!
 # Cubics and discriminants
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines cubic polynomials over a semiring and their discriminants over a splitting field.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

@@ -38,11 +38,13 @@ cubic, discriminant, polynomial, root
 
 noncomputable section
 
+#print Cubic /-
 /-- The structure representing a cubic polynomial. -/
 @[ext]
 structure Cubic (R : Type _) where
   (a b c d : R)
 #align cubic Cubic
+-/
 
 namespace Cubic
 
@@ -62,24 +64,38 @@ section Basic
 
 variable {P Q : Cubic R} {a b c d a' b' c' d' : R} [Semiring R]
 
+#print Cubic.toPoly /-
 /-- Convert a cubic polynomial to a polynomial. -/
 def toPoly (P : Cubic R) : R[X] :=
   C P.a * X ^ 3 + C P.b * X ^ 2 + C P.c * X + C P.d
 #align cubic.to_poly Cubic.toPoly
+-/
 
-theorem c_mul_prod_x_sub_c_eq [CommRing S] {w x y z : S} :
+/- warning: cubic.C_mul_prod_X_sub_C_eq -> Cubic.C_mul_prod_X_sub_C_eq is a dubious translation:
+lean 3 declaration is
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {w : S} {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S 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(CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) 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(Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (fun (_x : RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) => S -> (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.hasCoeToFun.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z))) (Cubic.toPoly.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)) (Cubic.mk.{u1} S w (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toHasAdd.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x z)) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) y z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) w (Neg.neg.{u1} S (SubNegMonoid.toHasNeg.{u1} S (AddGroup.toSubNegMonoid.{u1} S (AddGroupWithOne.toAddGroup.{u1} S (AddCommGroupWithOne.toAddGroupWithOne.{u1} S (Ring.toAddCommGroupWithOne.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (Distrib.toHasMul.{u1} S (Ring.toDistrib.{u1} S (CommRing.toRing.{u1} S _inst_2)))) x y) z)))))
+but is expected to have type
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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) w) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S 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S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) 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_inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S 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(Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S 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z))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) w (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HAdd.hAdd.{u1, u1, u1} S S S (instHAdd.{u1} S (Distrib.toAdd.{u1} S (NonUnitalNonAssocSemiring.toDistrib.{u1} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))))) (HMul.hMul.{u1, u1, u1} S S S (instHMul.{u1} S (NonUnitalNonAssocRing.toMul.{u1} S (NonAssocRing.toNonUnitalNonAssocRing.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_2))))) x y) (HMul.hMul.{u1, u1, u1} S S S 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(CommRing.toRing.{u1} S _inst_2))))) x y) z)))))
+Case conversion may be inaccurate. Consider using '#align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eqₓ'. -/
+theorem C_mul_prod_X_sub_C_eq [CommRing S] {w x y z : S} :
     C w * (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨w, w * -(x + y + z), w * (x * y + x * z + y * z), w * -(x * y * z)⟩ :=
   by
   simp only [to_poly, C_neg, C_add, C_mul]
   ring1
-#align cubic.C_mul_prod_X_sub_C_eq Cubic.c_mul_prod_x_sub_c_eq
-
-theorem prod_x_sub_c_eq [CommRing S] {x y z : S} :
+#align cubic.C_mul_prod_X_sub_C_eq Cubic.C_mul_prod_X_sub_C_eq
+
+/- warning: cubic.prod_X_sub_C_eq -> Cubic.prod_X_sub_C_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {S : Type.{u1}} [_inst_2 : CommRing.{u1} S] {x : S} {y : S} {z : S}, Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.mul'.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) x)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (RingHom.instRingHomClassRingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))))) (Polynomial.C.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) y))) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) z) (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (instHSub.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.sub.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.X.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Polynomial.semiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} S (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_2))) (Semiring.toNonAssocSemiring.{u1} 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+Case conversion may be inaccurate. Consider using '#align cubic.prod_X_sub_C_eq Cubic.prod_X_sub_C_eqₓ'. -/
+theorem prod_X_sub_C_eq [CommRing S] {x y z : S} :
     (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨1, -(x + y + z), x * y + x * z + y * z, -(x * y * z)⟩ :=
   by rw [← one_mul <| X - C x, ← C_1, C_mul_prod_X_sub_C_eq, one_mul, one_mul, one_mul]
-#align cubic.prod_X_sub_C_eq Cubic.prod_x_sub_c_eq
+#align cubic.prod_X_sub_C_eq Cubic.prod_X_sub_C_eq
 
 /-! ### Coefficients -/
 
@@ -99,83 +115,167 @@ private theorem coeffs :
   repeat' rw [zero_add]
 #align cubic.coeffs cubic.coeffs
 
+/- warning: cubic.coeff_eq_zero -> Cubic.coeff_eq_zero is a dubious translation:
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+but is expected to have type
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R] {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) n) -> (Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (Cubic.toPoly.{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)))))
+Case conversion may be inaccurate. Consider using '#align cubic.coeff_eq_zero Cubic.coeff_eq_zeroₓ'. -/
 @[simp]
 theorem coeff_eq_zero {n : ℕ} (hn : 3 < n) : P.toPoly.coeff n = 0 :=
   coeffs.1 n hn
 #align cubic.coeff_eq_zero Cubic.coeff_eq_zero
 
+#print Cubic.coeff_eq_a /-
 @[simp]
 theorem coeff_eq_a : P.toPoly.coeff 3 = P.a :=
   coeffs.2.1
 #align cubic.coeff_eq_a Cubic.coeff_eq_a
+-/
 
+#print Cubic.coeff_eq_b /-
 @[simp]
 theorem coeff_eq_b : P.toPoly.coeff 2 = P.b :=
   coeffs.2.2.1
 #align cubic.coeff_eq_b Cubic.coeff_eq_b
+-/
 
+#print Cubic.coeff_eq_c /-
 @[simp]
 theorem coeff_eq_c : P.toPoly.coeff 1 = P.c :=
   coeffs.2.2.2.1
 #align cubic.coeff_eq_c Cubic.coeff_eq_c
+-/
 
+#print Cubic.coeff_eq_d /-
 @[simp]
 theorem coeff_eq_d : P.toPoly.coeff 0 = P.d :=
   coeffs.2.2.2.2
 #align cubic.coeff_eq_d Cubic.coeff_eq_d
+-/
 
+#print Cubic.a_of_eq /-
 theorem a_of_eq (h : P.toPoly = Q.toPoly) : P.a = Q.a := by rw [← coeff_eq_a, h, coeff_eq_a]
 #align cubic.a_of_eq Cubic.a_of_eq
+-/
 
+#print Cubic.b_of_eq /-
 theorem b_of_eq (h : P.toPoly = Q.toPoly) : P.b = Q.b := by rw [← coeff_eq_b, h, coeff_eq_b]
 #align cubic.b_of_eq Cubic.b_of_eq
+-/
 
+#print Cubic.c_of_eq /-
 theorem c_of_eq (h : P.toPoly = Q.toPoly) : P.c = Q.c := by rw [← coeff_eq_c, h, coeff_eq_c]
 #align cubic.c_of_eq Cubic.c_of_eq
+-/
 
+#print Cubic.d_of_eq /-
 theorem d_of_eq (h : P.toPoly = Q.toPoly) : P.d = Q.d := by rw [← coeff_eq_d, h, coeff_eq_d]
 #align cubic.d_of_eq Cubic.d_of_eq
+-/
 
+#print Cubic.toPoly_injective /-
 theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
   ⟨fun h => ext P Q (a_of_eq h) (b_of_eq h) (c_of_eq h) (d_of_eq h), congr_arg toPoly⟩
 #align cubic.to_poly_injective Cubic.toPoly_injective
+-/
 
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+Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero Cubic.of_a_eq_zeroₓ'. -/
 theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
   rw [to_poly, ha, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_a_eq_zero Cubic.of_a_eq_zero
 
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+Case conversion may be inaccurate. Consider using '#align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'ₓ'. -/
 theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
   of_a_eq_zero rfl
 #align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'
 
+/- warning: cubic.of_b_eq_zero -> Cubic.of_b_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.of_b_eq_zero Cubic.of_b_eq_zeroₓ'. -/
 theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.d := by
   rw [of_a_eq_zero ha, hb, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_b_eq_zero Cubic.of_b_eq_zero
 
+/- warning: cubic.of_b_eq_zero' -> Cubic.of_b_eq_zero' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'ₓ'. -/
 theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
   of_b_eq_zero rfl rfl
 #align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'
 
+/- warning: cubic.of_c_eq_zero -> Cubic.of_c_eq_zero is a dubious translation:
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 theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C P.d := by
   rw [of_b_eq_zero ha hb, hc, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_c_eq_zero Cubic.of_c_eq_zero
 
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 theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = C d :=
   of_c_eq_zero rfl rfl rfl
 #align cubic.of_c_eq_zero' Cubic.of_c_eq_zero'
 
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 theorem of_d_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 0) : P.toPoly = 0 :=
   by rw [of_c_eq_zero ha hb hc, hd, C_0]
 #align cubic.of_d_eq_zero Cubic.of_d_eq_zero
 
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 theorem of_d_eq_zero' : (⟨0, 0, 0, 0⟩ : Cubic R).toPoly = 0 :=
   of_d_eq_zero rfl rfl rfl rfl
 #align cubic.of_d_eq_zero' Cubic.of_d_eq_zero'
 
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 theorem zero : (0 : Cubic R).toPoly = 0 :=
   of_d_eq_zero'
 #align cubic.zero Cubic.zero
 
+/- warning: cubic.to_poly_eq_zero_iff -> Cubic.toPoly_eq_zero_iff is a dubious translation:
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 theorem toPoly_eq_zero_iff (P : Cubic R) : P.toPoly = 0 ↔ P = 0 := by rw [← zero, to_poly_injective]
 #align cubic.to_poly_eq_zero_iff Cubic.toPoly_eq_zero_iff
 
@@ -186,62 +286,135 @@ private theorem ne_zero (h0 : P.a ≠ 0 ∨ P.b ≠ 0 ∨ P.c ≠ 0 ∨ P.d ≠
   exact ⟨rfl, rfl, rfl, rfl⟩
 #align cubic.ne_zero cubic.ne_zero
 
+/- warning: cubic.ne_zero_of_a_ne_zero -> Cubic.ne_zero_of_a_ne_zero is a dubious translation:
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 theorem ne_zero_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp NeZero).1 ha
 #align cubic.ne_zero_of_a_ne_zero Cubic.ne_zero_of_a_ne_zero
 
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 theorem ne_zero_of_b_ne_zero (hb : P.b ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp NeZero).2).1 hb
 #align cubic.ne_zero_of_b_ne_zero Cubic.ne_zero_of_b_ne_zero
 
+/- warning: cubic.ne_zero_of_c_ne_zero -> Cubic.ne_zero_of_c_ne_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.ne_zero_of_c_ne_zero Cubic.ne_zero_of_c_ne_zeroₓ'. -/
 theorem ne_zero_of_c_ne_zero (hc : P.c ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp (or_imp.mp NeZero).2).2).1 hc
 #align cubic.ne_zero_of_c_ne_zero Cubic.ne_zero_of_c_ne_zero
 
+/- warning: cubic.ne_zero_of_d_ne_zero -> Cubic.ne_zero_of_d_ne_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.ne_zero_of_d_ne_zero Cubic.ne_zero_of_d_ne_zeroₓ'. -/
 theorem ne_zero_of_d_ne_zero (hd : P.d ≠ 0) : P.toPoly ≠ 0 :=
   (or_imp.mp (or_imp.mp (or_imp.mp NeZero).2).2).2 hd
 #align cubic.ne_zero_of_d_ne_zero Cubic.ne_zero_of_d_ne_zero
 
+/- warning: cubic.leading_coeff_of_a_ne_zero -> Cubic.leadingCoeff_of_a_ne_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.leading_coeff_of_a_ne_zero Cubic.leadingCoeff_of_a_ne_zeroₓ'. -/
 @[simp]
 theorem leadingCoeff_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.leadingCoeff = P.a :=
   leadingCoeff_cubic ha
 #align cubic.leading_coeff_of_a_ne_zero Cubic.leadingCoeff_of_a_ne_zero
 
+/- warning: cubic.leading_coeff_of_a_ne_zero' -> Cubic.leadingCoeff_of_a_ne_zero' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.leading_coeff_of_a_ne_zero' Cubic.leadingCoeff_of_a_ne_zero'ₓ'. -/
 @[simp]
 theorem leadingCoeff_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).leadingCoeff = a :=
   leadingCoeff_of_a_ne_zero ha
 #align cubic.leading_coeff_of_a_ne_zero' Cubic.leadingCoeff_of_a_ne_zero'
 
+/- warning: cubic.leading_coeff_of_b_ne_zero -> Cubic.leadingCoeff_of_b_ne_zero is a dubious translation:
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 @[simp]
 theorem leadingCoeff_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.leadingCoeff = P.b := by
   rw [of_a_eq_zero ha, leading_coeff_quadratic hb]
 #align cubic.leading_coeff_of_b_ne_zero Cubic.leadingCoeff_of_b_ne_zero
 
+/- warning: cubic.leading_coeff_of_b_ne_zero' -> Cubic.leadingCoeff_of_b_ne_zero' is a dubious translation:
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 @[simp]
 theorem leadingCoeff_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).leadingCoeff = b :=
   leadingCoeff_of_b_ne_zero rfl hb
 #align cubic.leading_coeff_of_b_ne_zero' Cubic.leadingCoeff_of_b_ne_zero'
 
+/- warning: cubic.leading_coeff_of_c_ne_zero -> Cubic.leadingCoeff_of_c_ne_zero is a dubious translation:
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 @[simp]
 theorem leadingCoeff_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) :
     P.toPoly.leadingCoeff = P.c := by rw [of_b_eq_zero ha hb, leading_coeff_linear hc]
 #align cubic.leading_coeff_of_c_ne_zero Cubic.leadingCoeff_of_c_ne_zero
 
+/- warning: cubic.leading_coeff_of_c_ne_zero' -> Cubic.leadingCoeff_of_c_ne_zero' is a dubious translation:
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 @[simp]
 theorem leadingCoeff_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).leadingCoeff = c :=
   leadingCoeff_of_c_ne_zero rfl rfl hc
 #align cubic.leading_coeff_of_c_ne_zero' Cubic.leadingCoeff_of_c_ne_zero'
 
+/- warning: cubic.leading_coeff_of_c_eq_zero -> Cubic.leadingCoeff_of_c_eq_zero is a dubious translation:
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 @[simp]
 theorem leadingCoeff_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
     P.toPoly.leadingCoeff = P.d := by rw [of_c_eq_zero ha hb hc, leading_coeff_C]
 #align cubic.leading_coeff_of_c_eq_zero Cubic.leadingCoeff_of_c_eq_zero
 
+/- warning: cubic.leading_coeff_of_c_eq_zero' -> Cubic.leadingCoeff_of_c_eq_zero' is a dubious translation:
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+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) (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))))))) d))) d
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+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{succ u1} R (Polynomial.leadingCoeff.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) d))) d
+Case conversion may be inaccurate. Consider using '#align cubic.leading_coeff_of_c_eq_zero' Cubic.leadingCoeff_of_c_eq_zero'ₓ'. -/
 @[simp]
 theorem leadingCoeff_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).leadingCoeff = d :=
   leadingCoeff_of_c_eq_zero rfl rfl rfl
 #align cubic.leading_coeff_of_c_eq_zero' Cubic.leadingCoeff_of_c_eq_zero'
 
+#print Cubic.monic_of_a_eq_one /-
 theorem monic_of_a_eq_one (ha : P.a = 1) : P.toPoly.Monic :=
   by
   nontriviality
@@ -251,11 +424,20 @@ theorem monic_of_a_eq_one (ha : P.a = 1) : P.toPoly.Monic :=
       exact one_ne_zero,
     ha]
 #align cubic.monic_of_a_eq_one Cubic.monic_of_a_eq_one
+-/
 
+#print Cubic.monic_of_a_eq_one' /-
 theorem monic_of_a_eq_one' : (toPoly ⟨1, b, c, d⟩).Monic :=
   monic_of_a_eq_one rfl
 #align cubic.monic_of_a_eq_one' Cubic.monic_of_a_eq_one'
+-/
 
+/- warning: cubic.monic_of_b_eq_one -> Cubic.monic_of_b_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P))
+but is expected to have type
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P))
+Case conversion may be inaccurate. Consider using '#align cubic.monic_of_b_eq_one Cubic.monic_of_b_eq_oneₓ'. -/
 theorem monic_of_b_eq_one (ha : P.a = 0) (hb : P.b = 1) : P.toPoly.Monic :=
   by
   nontriviality
@@ -266,10 +448,22 @@ theorem monic_of_b_eq_one (ha : P.a = 0) (hb : P.b = 1) : P.toPoly.Monic :=
     hb]
 #align cubic.monic_of_b_eq_one Cubic.monic_of_b_eq_one
 
+/- warning: cubic.monic_of_b_eq_one' -> Cubic.monic_of_b_eq_one' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) c d))
+but is expected to have type
+  forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) c d))
+Case conversion may be inaccurate. Consider using '#align cubic.monic_of_b_eq_one' Cubic.monic_of_b_eq_one'ₓ'. -/
 theorem monic_of_b_eq_one' : (toPoly ⟨0, 1, c, d⟩).Monic :=
   monic_of_b_eq_one rfl rfl
 #align cubic.monic_of_b_eq_one' Cubic.monic_of_b_eq_one'
 
+/- warning: cubic.monic_of_c_eq_one -> Cubic.monic_of_c_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P))
+but is expected to have type
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P))
+Case conversion may be inaccurate. Consider using '#align cubic.monic_of_c_eq_one Cubic.monic_of_c_eq_oneₓ'. -/
 theorem monic_of_c_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 1) : P.toPoly.Monic :=
   by
   nontriviality
@@ -280,17 +474,31 @@ theorem monic_of_c_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 1) : P.toPol
     hc]
 #align cubic.monic_of_c_eq_one Cubic.monic_of_c_eq_one
 
+/- warning: cubic.monic_of_c_eq_one' -> Cubic.monic_of_c_eq_one' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) d))
+but is expected to have type
+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1))) d))
+Case conversion may be inaccurate. Consider using '#align cubic.monic_of_c_eq_one' Cubic.monic_of_c_eq_one'ₓ'. -/
 theorem monic_of_c_eq_one' : (toPoly ⟨0, 0, 1, d⟩).Monic :=
   monic_of_c_eq_one rfl rfl rfl
 #align cubic.monic_of_c_eq_one' Cubic.monic_of_c_eq_one'
 
+/- warning: cubic.monic_of_d_eq_one -> Cubic.monic_of_d_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.d.{u1} R P) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P))
+but is expected to have type
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.d.{u1} R P) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R _inst_1)))) -> (Polynomial.Monic.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P))
+Case conversion may be inaccurate. Consider using '#align cubic.monic_of_d_eq_one Cubic.monic_of_d_eq_oneₓ'. -/
 theorem monic_of_d_eq_one (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 1) :
     P.toPoly.Monic := by rw [monic, leading_coeff_of_c_eq_zero ha hb hc, hd]
 #align cubic.monic_of_d_eq_one Cubic.monic_of_d_eq_one
 
+#print Cubic.monic_of_d_eq_one' /-
 theorem monic_of_d_eq_one' : (toPoly ⟨0, 0, 0, 1⟩).Monic :=
   monic_of_d_eq_one rfl rfl rfl rfl
 #align cubic.monic_of_d_eq_one' Cubic.monic_of_d_eq_one'
+-/
 
 end Coeff
 
@@ -299,6 +507,7 @@ end Coeff
 
 section Degree
 
+#print Cubic.equiv /-
 /-- The equivalence between cubic polynomials and polynomials of degree at most three. -/
 @[simps]
 def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
@@ -312,142 +521,323 @@ def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 }
     rw [coeff_eq_zero h3,
       (degree_le_iff_coeff_zero (f : R[X]) 3).mp f.2 _ <| with_bot.coe_lt_coe.mpr h3]
 #align cubic.equiv Cubic.equiv
+-/
 
+/- warning: cubic.degree_of_a_ne_zero -> Cubic.degree_of_a_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Ne.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 3 (OfNat.mk.{0} (WithBot.{0} Nat) 3 (bit1.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne) (WithBot.hasAdd.{0} Nat Nat.hasAdd) (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne))))))
+but is expected to have type
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Ne.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} (WithBot.{0} Nat) 3 (instOfNat.{0} (WithBot.{0} Nat) 3 (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)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_a_ne_zero Cubic.degree_of_a_ne_zeroₓ'. -/
 @[simp]
 theorem degree_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.degree = 3 :=
   degree_cubic ha
 #align cubic.degree_of_a_ne_zero Cubic.degree_of_a_ne_zero
 
+/- warning: cubic.degree_of_a_ne_zero' -> Cubic.degree_of_a_ne_zero' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {a : R} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R a b c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 3 (OfNat.mk.{0} (WithBot.{0} Nat) 3 (bit1.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne) (WithBot.hasAdd.{0} Nat Nat.hasAdd) (One.one.{0} (WithBot.{0} Nat) (WithBot.hasOne.{0} Nat Nat.hasOne))))))
+but is expected to have type
+  forall {R : Type.{u1}} {a : R} {b : R} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], (Ne.{succ u1} R a (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} (WithBot.{0} Nat) (Polynomial.degree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R a b c d))) (OfNat.ofNat.{0} (WithBot.{0} Nat) 3 (instOfNat.{0} (WithBot.{0} Nat) 3 (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)))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_a_ne_zero' Cubic.degree_of_a_ne_zero'ₓ'. -/
 @[simp]
 theorem degree_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).degree = 3 :=
   degree_of_a_ne_zero ha
 #align cubic.degree_of_a_ne_zero' Cubic.degree_of_a_ne_zero'
 
+/- warning: cubic.degree_of_a_eq_zero -> Cubic.degree_of_a_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_a_eq_zero Cubic.degree_of_a_eq_zeroₓ'. -/
 theorem degree_of_a_eq_zero (ha : P.a = 0) : P.toPoly.degree ≤ 2 := by
   simpa only [of_a_eq_zero ha] using degree_quadratic_le
 #align cubic.degree_of_a_eq_zero Cubic.degree_of_a_eq_zero
 
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+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_a_eq_zero' Cubic.degree_of_a_eq_zero'ₓ'. -/
 theorem degree_of_a_eq_zero' : (toPoly ⟨0, b, c, d⟩).degree ≤ 2 :=
   degree_of_a_eq_zero rfl
 #align cubic.degree_of_a_eq_zero' Cubic.degree_of_a_eq_zero'
 
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+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_b_ne_zero Cubic.degree_of_b_ne_zeroₓ'. -/
 @[simp]
 theorem degree_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.degree = 2 := by
   rw [of_a_eq_zero ha, degree_quadratic hb]
 #align cubic.degree_of_b_ne_zero Cubic.degree_of_b_ne_zero
 
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 @[simp]
 theorem degree_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).degree = 2 :=
   degree_of_b_ne_zero rfl hb
 #align cubic.degree_of_b_ne_zero' Cubic.degree_of_b_ne_zero'
 
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 theorem degree_of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly.degree ≤ 1 := by
   simpa only [of_b_eq_zero ha hb] using degree_linear_le
 #align cubic.degree_of_b_eq_zero Cubic.degree_of_b_eq_zero
 
+/- warning: cubic.degree_of_b_eq_zero' -> Cubic.degree_of_b_eq_zero' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_b_eq_zero' Cubic.degree_of_b_eq_zero'ₓ'. -/
 theorem degree_of_b_eq_zero' : (toPoly ⟨0, 0, c, d⟩).degree ≤ 1 :=
   degree_of_b_eq_zero rfl rfl
 #align cubic.degree_of_b_eq_zero' Cubic.degree_of_b_eq_zero'
 
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 @[simp]
 theorem degree_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) : P.toPoly.degree = 1 := by
   rw [of_b_eq_zero ha hb, degree_linear hc]
 #align cubic.degree_of_c_ne_zero Cubic.degree_of_c_ne_zero
 
+/- warning: cubic.degree_of_c_ne_zero' -> Cubic.degree_of_c_ne_zero' is a dubious translation:
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 @[simp]
 theorem degree_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).degree = 1 :=
   degree_of_c_ne_zero rfl rfl hc
 #align cubic.degree_of_c_ne_zero' Cubic.degree_of_c_ne_zero'
 
+/- warning: cubic.degree_of_c_eq_zero -> Cubic.degree_of_c_eq_zero is a dubious translation:
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 theorem degree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly.degree ≤ 0 := by
   simpa only [of_c_eq_zero ha hb hc] using degree_C_le
 #align cubic.degree_of_c_eq_zero Cubic.degree_of_c_eq_zero
 
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 theorem degree_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).degree ≤ 0 :=
   degree_of_c_eq_zero rfl rfl rfl
 #align cubic.degree_of_c_eq_zero' Cubic.degree_of_c_eq_zero'
 
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 @[simp]
 theorem degree_of_d_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d ≠ 0) :
     P.toPoly.degree = 0 := by rw [of_c_eq_zero ha hb hc, degree_C hd]
 #align cubic.degree_of_d_ne_zero Cubic.degree_of_d_ne_zero
 
+/- warning: cubic.degree_of_d_ne_zero' -> Cubic.degree_of_d_ne_zero' is a dubious translation:
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 @[simp]
 theorem degree_of_d_ne_zero' (hd : d ≠ 0) : (toPoly ⟨0, 0, 0, d⟩).degree = 0 :=
   degree_of_d_ne_zero rfl rfl rfl hd
 #align cubic.degree_of_d_ne_zero' Cubic.degree_of_d_ne_zero'
 
+/- warning: cubic.degree_of_d_eq_zero -> Cubic.degree_of_d_eq_zero is a dubious translation:
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 @[simp]
 theorem degree_of_d_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P.d = 0) :
     P.toPoly.degree = ⊥ := by rw [of_d_eq_zero ha hb hc hd, degree_zero]
 #align cubic.degree_of_d_eq_zero Cubic.degree_of_d_eq_zero
 
+/- warning: cubic.degree_of_d_eq_zero' -> Cubic.degree_of_d_eq_zero' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_d_eq_zero' Cubic.degree_of_d_eq_zero'ₓ'. -/
 @[simp]
 theorem degree_of_d_eq_zero' : (⟨0, 0, 0, 0⟩ : Cubic R).toPoly.degree = ⊥ :=
   degree_of_d_eq_zero rfl rfl rfl rfl
 #align cubic.degree_of_d_eq_zero' Cubic.degree_of_d_eq_zero'
 
+/- warning: cubic.degree_of_zero -> Cubic.degree_of_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.degree_of_zero Cubic.degree_of_zeroₓ'. -/
 @[simp]
 theorem degree_of_zero : (0 : Cubic R).toPoly.degree = ⊥ :=
   degree_of_d_eq_zero'
 #align cubic.degree_of_zero Cubic.degree_of_zero
 
+/- warning: cubic.nat_degree_of_a_ne_zero -> Cubic.natDegree_of_a_ne_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_a_ne_zero Cubic.natDegree_of_a_ne_zeroₓ'. -/
 @[simp]
 theorem natDegree_of_a_ne_zero (ha : P.a ≠ 0) : P.toPoly.natDegree = 3 :=
   natDegree_cubic ha
 #align cubic.nat_degree_of_a_ne_zero Cubic.natDegree_of_a_ne_zero
 
+/- warning: cubic.nat_degree_of_a_ne_zero' -> Cubic.natDegree_of_a_ne_zero' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_a_ne_zero' Cubic.natDegree_of_a_ne_zero'ₓ'. -/
 @[simp]
 theorem natDegree_of_a_ne_zero' (ha : a ≠ 0) : (toPoly ⟨a, b, c, d⟩).natDegree = 3 :=
   natDegree_of_a_ne_zero ha
 #align cubic.nat_degree_of_a_ne_zero' Cubic.natDegree_of_a_ne_zero'
 
+/- warning: cubic.nat_degree_of_a_eq_zero -> Cubic.natDegree_of_a_eq_zero is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_a_eq_zero Cubic.natDegree_of_a_eq_zeroₓ'. -/
 theorem natDegree_of_a_eq_zero (ha : P.a = 0) : P.toPoly.natDegree ≤ 2 := by
   simpa only [of_a_eq_zero ha] using nat_degree_quadratic_le
 #align cubic.nat_degree_of_a_eq_zero Cubic.natDegree_of_a_eq_zero
 
+/- warning: cubic.nat_degree_of_a_eq_zero' -> Cubic.natDegree_of_a_eq_zero' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_a_eq_zero' Cubic.natDegree_of_a_eq_zero'ₓ'. -/
 theorem natDegree_of_a_eq_zero' : (toPoly ⟨0, b, c, d⟩).natDegree ≤ 2 :=
   natDegree_of_a_eq_zero rfl
 #align cubic.nat_degree_of_a_eq_zero' Cubic.natDegree_of_a_eq_zero'
 
+/- warning: cubic.nat_degree_of_b_ne_zero -> Cubic.natDegree_of_b_ne_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_b_ne_zero Cubic.natDegree_of_b_ne_zeroₓ'. -/
 @[simp]
 theorem natDegree_of_b_ne_zero (ha : P.a = 0) (hb : P.b ≠ 0) : P.toPoly.natDegree = 2 := by
   rw [of_a_eq_zero ha, nat_degree_quadratic hb]
 #align cubic.nat_degree_of_b_ne_zero Cubic.natDegree_of_b_ne_zero
 
+/- warning: cubic.nat_degree_of_b_ne_zero' -> Cubic.natDegree_of_b_ne_zero' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_b_ne_zero' Cubic.natDegree_of_b_ne_zero'ₓ'. -/
 @[simp]
 theorem natDegree_of_b_ne_zero' (hb : b ≠ 0) : (toPoly ⟨0, b, c, d⟩).natDegree = 2 :=
   natDegree_of_b_ne_zero rfl hb
 #align cubic.nat_degree_of_b_ne_zero' Cubic.natDegree_of_b_ne_zero'
 
+/- warning: cubic.nat_degree_of_b_eq_zero -> Cubic.natDegree_of_b_eq_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_b_eq_zero Cubic.natDegree_of_b_eq_zeroₓ'. -/
 theorem natDegree_of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly.natDegree ≤ 1 := by
   simpa only [of_b_eq_zero ha hb] using nat_degree_linear_le
 #align cubic.nat_degree_of_b_eq_zero Cubic.natDegree_of_b_eq_zero
 
+/- warning: cubic.nat_degree_of_b_eq_zero' -> Cubic.natDegree_of_b_eq_zero' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_b_eq_zero' Cubic.natDegree_of_b_eq_zero'ₓ'. -/
 theorem natDegree_of_b_eq_zero' : (toPoly ⟨0, 0, c, d⟩).natDegree ≤ 1 :=
   natDegree_of_b_eq_zero rfl rfl
 #align cubic.nat_degree_of_b_eq_zero' Cubic.natDegree_of_b_eq_zero'
 
+/- warning: cubic.nat_degree_of_c_ne_zero -> Cubic.natDegree_of_c_ne_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_c_ne_zero Cubic.natDegree_of_c_ne_zeroₓ'. -/
 @[simp]
 theorem natDegree_of_c_ne_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c ≠ 0) :
     P.toPoly.natDegree = 1 := by rw [of_b_eq_zero ha hb, nat_degree_linear hc]
 #align cubic.nat_degree_of_c_ne_zero Cubic.natDegree_of_c_ne_zero
 
+/- warning: cubic.nat_degree_of_c_ne_zero' -> Cubic.natDegree_of_c_ne_zero' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} {c : R} {d : R} [_inst_1 : Semiring.{u1} R], (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) c d))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))
+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_c_ne_zero' Cubic.natDegree_of_c_ne_zero'ₓ'. -/
 @[simp]
 theorem natDegree_of_c_ne_zero' (hc : c ≠ 0) : (toPoly ⟨0, 0, c, d⟩).natDegree = 1 :=
   natDegree_of_c_ne_zero rfl rfl hc
 #align cubic.nat_degree_of_c_ne_zero' Cubic.natDegree_of_c_ne_zero'
 
+/- warning: cubic.nat_degree_of_c_eq_zero -> Cubic.natDegree_of_c_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall {R : Type.{u1}} {P : Cubic.{u1} R} [_inst_1 : Semiring.{u1} R], (Eq.{succ u1} R (Cubic.a.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.b.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{succ u1} R (Cubic.c.{u1} R P) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 P)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_c_eq_zero Cubic.natDegree_of_c_eq_zeroₓ'. -/
 @[simp]
 theorem natDegree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
     P.toPoly.natDegree = 0 := by rw [of_c_eq_zero ha hb hc, nat_degree_C]
 #align cubic.nat_degree_of_c_eq_zero Cubic.natDegree_of_c_eq_zero
 
+/- warning: cubic.nat_degree_of_c_eq_zero' -> Cubic.natDegree_of_c_eq_zero' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (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))))))) (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))))))) (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))))))) d))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
+but is expected to have type
+  forall {R : Type.{u1}} {d : R} [_inst_1 : Semiring.{u1} R], Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (Cubic.mk.{u1} R (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) d))) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))
+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_c_eq_zero' Cubic.natDegree_of_c_eq_zero'ₓ'. -/
 @[simp]
 theorem natDegree_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).natDegree = 0 :=
   natDegree_of_c_eq_zero rfl rfl rfl
 #align cubic.nat_degree_of_c_eq_zero' Cubic.natDegree_of_c_eq_zero'
 
+/- warning: cubic.nat_degree_of_zero -> Cubic.natDegree_of_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R], Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (Cubic.toPoly.{u1} R _inst_1 (OfNat.ofNat.{u1} (Cubic.{u1} R) 0 (OfNat.mk.{u1} (Cubic.{u1} R) 0 (Zero.zero.{u1} (Cubic.{u1} R) (Cubic.hasZero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))
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+Case conversion may be inaccurate. Consider using '#align cubic.nat_degree_of_zero Cubic.natDegree_of_zeroₓ'. -/
 @[simp]
 theorem natDegree_of_zero : (0 : Cubic R).toPoly.natDegree = 0 :=
   natDegree_of_c_eq_zero'
@@ -462,14 +852,18 @@ section Map
 
 variable [Semiring S] {φ : R →+* S}
 
+#print Cubic.map /-
 /-- Map a cubic polynomial across a semiring homomorphism. -/
 def map (φ : R →+* S) (P : Cubic R) : Cubic S :=
   ⟨φ P.a, φ P.b, φ P.c, φ P.d⟩
 #align cubic.map Cubic.map
+-/
 
+#print Cubic.map_toPoly /-
 theorem map_toPoly : (map φ P).toPoly = Polynomial.map φ P.toPoly := by
   simp only [map, to_poly, map_C, map_X, Polynomial.map_add, Polynomial.map_mul, Polynomial.map_pow]
 #align cubic.map_to_poly Cubic.map_toPoly
+-/
 
 end Map
 
@@ -486,15 +880,25 @@ section Extension
 
 variable {P : Cubic R} [CommRing R] [CommRing S] {φ : R →+* S}
 
+#print Cubic.roots /-
 /-- The roots of a cubic polynomial. -/
 def roots [IsDomain R] (P : Cubic R) : Multiset R :=
   P.toPoly.roots
 #align cubic.roots Cubic.roots
+-/
 
+#print Cubic.map_roots /-
 theorem map_roots [IsDomain S] : (map φ P).roots = (Polynomial.map φ P.toPoly).roots := by
   rw [roots, map_to_poly]
 #align cubic.map_roots Cubic.map_roots
+-/
 
+/- warning: cubic.mem_roots_iff -> Cubic.mem_roots_iff is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.mem_roots_iff Cubic.mem_roots_iffₓ'. -/
 theorem mem_roots_iff [IsDomain R] (h0 : P.toPoly ≠ 0) (x : R) :
     x ∈ P.roots ↔ P.a * x ^ 3 + P.b * x ^ 2 + P.c * x + P.d = 0 :=
   by
@@ -502,6 +906,7 @@ theorem mem_roots_iff [IsDomain R] (h0 : P.toPoly ≠ 0) (x : R) :
   simp only [eval_C, eval_X, eval_add, eval_mul, eval_pow]
 #align cubic.mem_roots_iff Cubic.mem_roots_iff
 
+#print Cubic.card_roots_le /-
 theorem card_roots_le [IsDomain R] [DecidableEq R] : P.roots.toFinset.card ≤ 3 :=
   by
   apply (to_finset_card_le P.to_poly.roots).trans
@@ -514,6 +919,7 @@ theorem card_roots_le [IsDomain R] [DecidableEq R] : P.roots.toFinset.card ≤ 3
           exact zero_le 3)
   · exact WithBot.coe_le_coe.1 ((card_roots hP).trans degree_cubic_le)
 #align cubic.card_roots_le Cubic.card_roots_le
+-/
 
 end Extension
 
@@ -524,6 +930,12 @@ variable {P : Cubic F} [Field F] [Field K] {φ : F →+* K} {x y z : K}
 
 section Split
 
+/- warning: cubic.splits_iff_card_roots -> Cubic.splits_iff_card_roots is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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P))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Multiset.{u1} K) => Nat) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P))) 3 (instOfNatNat 3))))
+Case conversion may be inaccurate. Consider using '#align cubic.splits_iff_card_roots Cubic.splits_iff_card_rootsₓ'. -/
 theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ P).roots.card = 3 :=
   by
   replace ha : (map φ P).a ≠ 0 := (_root_.map_ne_zero φ).mpr ha
@@ -532,11 +944,23 @@ theorem splits_iff_card_roots (ha : P.a ≠ 0) : Splits φ P.toPoly ↔ (map φ
     ((degree_eq_iff_nat_degree_eq <| ne_zero_of_a_ne_zero ha).mp <| degree_of_a_ne_zero ha : _ = 3)]
 #align cubic.splits_iff_card_roots Cubic.splits_iff_card_roots
 
+/- warning: cubic.splits_iff_roots_eq_three -> Cubic.splits_iff_roots_eq_three is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_threeₓ'. -/
 theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
     Splits φ P.toPoly ↔ ∃ x y z : K, (map φ P).roots = {x, y, z} := by
   rw [splits_iff_card_roots ha, card_eq_three]
 #align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_three
 
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(Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (fun (_x : RingHom.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) => K -> (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (RingHom.hasCoeToFun.{u2, u2} K (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) (Polynomial.semiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))) (Polynomial.C.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))) z))))
+but is expected to have type
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Cubic.toPoly.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => 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_inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (a : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) a) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K 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(NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) 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(NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) 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(NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P))) (Polynomial.mul'.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (fun (_x : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) => Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))) (Polynomial.semiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) 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_inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))) (RingHom.instRingHomClassRingHom.{u1, u1} K (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) (Polynomial.semiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))))))))) (Polynomial.C.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2)))) z))))
+Case conversion may be inaccurate. Consider using '#align cubic.eq_prod_three_roots Cubic.eq_prod_three_rootsₓ'. -/
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
   by
@@ -548,6 +972,12 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
   rw [prod_cons, prod_cons, prod_singleton, mul_assoc, mul_assoc]
 #align cubic.eq_prod_three_roots Cubic.eq_prod_three_roots
 
+/- warning: cubic.eq_sum_three_roots -> Cubic.eq_sum_three_roots is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, 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(DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K 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K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x z)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) y z))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (Neg.neg.{u2} K (SubNegMonoid.toHasNeg.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) z)))))
+but is expected to have type
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P)) (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) x (Insert.insert.{u1, u1} K (Multiset.{u1} K) (Multiset.instInsertMultiset.{u1} K) y (Singleton.singleton.{u1, u1} K (Multiset.{u1} K) (Multiset.instSingletonMultiset.{u1} K) z)))) -> (Eq.{succ u1} (Cubic.{u1} K) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F (Semifield.toDivisionSemiring.{u2} F (Field.toSemifield.{u2} F _inst_1))) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_2))) φ P) (Cubic.mk.{u1} K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonUnitalNonAssocSemiring.toMul.{u2} F (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) K ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (DivisionRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) (Field.toDivisionRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) _inst_2)))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F (fun 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(DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (Neg.neg.{u1} K (Ring.toNeg.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) z)))))
+Case conversion may be inaccurate. Consider using '#align cubic.eq_sum_three_roots Cubic.eq_sum_three_rootsₓ'. -/
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
       ⟨φ P.a, φ P.a * -(x + y + z), φ P.a * (x * y + x * z + y * z), φ P.a * -(x * y * z)⟩ :=
@@ -557,14 +987,32 @@ theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
   rw [eq_prod_three_roots ha h3, C_mul_prod_X_sub_C_eq]
 #align cubic.eq_sum_three_roots Cubic.eq_sum_three_roots
 
+/- warning: cubic.b_eq_three_roots -> Cubic.b_eq_three_roots is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cubic.b_eq_three_roots Cubic.b_eq_three_rootsₓ'. -/
 theorem b_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.b = φ P.a * -(x + y + z) := by injection eq_sum_three_roots ha h3
 #align cubic.b_eq_three_roots Cubic.b_eq_three_roots
 
+/- warning: cubic.c_eq_three_roots -> Cubic.c_eq_three_roots is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.c.{u1} F P)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (fun (_x : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) => F -> K) (RingHom.hasCoeToFun.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) φ (Cubic.a.{u1} F P)) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HAdd.hAdd.{u2, u2, u2} K K K (instHAdd.{u2} K (Distrib.toHasAdd.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x y) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) x z)) (HMul.hMul.{u2, u2, u2} K K K (instHMul.{u2} K (Distrib.toHasMul.{u2} K (Ring.toDistrib.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))) y z))))
+but is expected to have type
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(Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F 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F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.a.{u2} F P)) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HAdd.hAdd.{u1, u1, u1} K K K (instHAdd.{u1} K (Distrib.toAdd.{u1} K (NonUnitalNonAssocSemiring.toDistrib.{u1} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x y) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) x z)) (HMul.hMul.{u1, u1, u1} K K K (instHMul.{u1} K (NonUnitalNonAssocRing.toMul.{u1} K (NonAssocRing.toNonUnitalNonAssocRing.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))) y z))))
+Case conversion may be inaccurate. Consider using '#align cubic.c_eq_three_roots Cubic.c_eq_three_rootsₓ'. -/
 theorem c_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.c = φ P.a * (x * y + x * z + y * z) := by injection eq_sum_three_roots ha h3
 #align cubic.c_eq_three_roots Cubic.c_eq_three_roots
 
+/- warning: cubic.d_eq_three_roots -> Cubic.d_eq_three_roots is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cubic.d_eq_three_roots Cubic.d_eq_three_rootsₓ'. -/
 theorem d_eq_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.d = φ P.a * -(x * y * z) := by injection eq_sum_three_roots ha h3
 #align cubic.d_eq_three_roots Cubic.d_eq_three_roots
@@ -576,12 +1024,20 @@ end Split
 
 section Discriminant
 
+#print Cubic.disc /-
 /-- The discriminant of a cubic polynomial. -/
 def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
   P.b ^ 2 * P.c ^ 2 - 4 * P.a * P.c ^ 3 - 4 * P.b ^ 3 * P.d - 27 * P.a ^ 2 * P.d ^ 2 +
     18 * P.a * P.b * P.c * P.d
 #align cubic.disc Cubic.disc
+-/
 
+/- warning: cubic.disc_eq_prod_three_roots -> Cubic.disc_eq_prod_three_roots is a dubious translation:
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(Field.toDivisionRing.{u2} K _inst_2)))))))) x z)) (HSub.hSub.{u2, u2, u2} K K K (instHSub.{u2} K (SubNegMonoid.toHasSub.{u2} K (AddGroup.toSubNegMonoid.{u2} K (AddGroupWithOne.toAddGroup.{u2} K (AddCommGroupWithOne.toAddGroupWithOne.{u2} K (Ring.toAddCommGroupWithOne.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2)))))))) y z)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
+but is expected to have type
+  forall {F : Type.{u2}} {K : Type.{u1}} {P : Cubic.{u2} F} [_inst_1 : Field.{u2} F] [_inst_2 : Field.{u1} K] {φ : RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))} {x : K} {y : K} {z : K}, (Ne.{succ u2} F (Cubic.a.{u2} F P) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (CommMonoidWithZero.toZero.{u2} F (CommGroupWithZero.toCommMonoidWithZero.{u2} F (Semifield.toCommGroupWithZero.{u2} F (Field.toSemifield.{u2} F _inst_1))))))) -> (Eq.{succ u1} (Multiset.{u1} K) (Cubic.roots.{u1} K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_2)) (Cubic.map.{u2, u1} F K (DivisionSemiring.toSemiring.{u2} F 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(Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} F (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2))))) F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))) (RingHom.instRingHomClassRingHom.{u2, u1} F K (NonAssocRing.toNonAssocSemiring.{u2} F (Ring.toNonAssocRing.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_2)))))))) φ (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.a.{u2} F P)) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : F) => K) (Cubic.disc.{u2} F (DivisionRing.toRing.{u2} F (Field.toDivisionRing.{u2} F _inst_1)) P)) (instHPow.{u1, 0} ((fun 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+Case conversion may be inaccurate. Consider using '#align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_rootsₓ'. -/
 theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     φ P.disc = (φ P.a * φ P.a * (x - y) * (x - z) * (y - z)) ^ 2 :=
   by
@@ -591,6 +1047,12 @@ theorem disc_eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y
   ring1
 #align cubic.disc_eq_prod_three_roots Cubic.disc_eq_prod_three_roots
 
+/- warning: cubic.disc_ne_zero_iff_roots_ne -> Cubic.disc_ne_zero_iff_roots_ne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cubic.disc_ne_zero_iff_roots_ne Cubic.disc_ne_zero_iff_roots_neₓ'. -/
 theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ x ≠ y ∧ x ≠ z ∧ y ≠ z :=
   by
@@ -599,6 +1061,12 @@ theorem disc_ne_zero_iff_roots_ne (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x,
     and_assoc']
 #align cubic.disc_ne_zero_iff_roots_ne Cubic.disc_ne_zero_iff_roots_ne
 
+/- warning: cubic.disc_ne_zero_iff_roots_nodup -> Cubic.disc_ne_zero_iff_roots_nodup is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cubic.disc_ne_zero_iff_roots_nodup Cubic.disc_ne_zero_iff_roots_nodupₓ'. -/
 theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     P.disc ≠ 0 ↔ (map φ P).roots.Nodup :=
   by
@@ -609,6 +1077,12 @@ theorem disc_ne_zero_iff_roots_nodup (ha : P.a ≠ 0) (h3 : (map φ P).roots = {
   tauto
 #align cubic.disc_ne_zero_iff_roots_nodup Cubic.disc_ne_zero_iff_roots_nodup
 
+/- warning: cubic.card_roots_of_disc_ne_zero -> Cubic.card_roots_of_disc_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.hasInsert.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.hasSingleton.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (OfNat.mk.{u1} F 0 (Zero.zero.{u1} F (MulZeroClass.toHasZero.{u1} F (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} F (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} F (NonAssocRing.toNonUnitalNonAssocRing.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))))))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Field.isDomain.{u2} K _inst_2) (Cubic.map.{u1, u2} F K (Ring.toSemiring.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
+but is expected to have type
+  forall {F : Type.{u1}} {K : Type.{u2}} {P : Cubic.{u1} F} [_inst_1 : Field.{u1} F] [_inst_2 : Field.{u2} K] {φ : RingHom.{u1, u2} F K (NonAssocRing.toNonAssocSemiring.{u1} F (Ring.toNonAssocRing.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_2))))} {x : K} {y : K} {z : K} [_inst_3 : DecidableEq.{succ u2} K], (Ne.{succ u1} F (Cubic.a.{u1} F P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{succ u2} (Multiset.{u2} K) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)) (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) x (Insert.insert.{u2, u2} K (Multiset.{u2} K) (Multiset.instInsertMultiset.{u2} K) y (Singleton.singleton.{u2, u2} K (Multiset.{u2} K) (Multiset.instSingletonMultiset.{u2} K) z)))) -> (Ne.{succ u1} F (Cubic.disc.{u1} F (DivisionRing.toRing.{u1} F (Field.toDivisionRing.{u1} F _inst_1)) P) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (CommMonoidWithZero.toZero.{u1} F (CommGroupWithZero.toCommMonoidWithZero.{u1} F (Semifield.toCommGroupWithZero.{u1} F (Field.toSemifield.{u1} F _inst_1))))))) -> (Eq.{1} Nat (Finset.card.{u2} K (Multiset.toFinset.{u2} K (fun (a : K) (b : K) => _inst_3 a b) (Cubic.roots.{u2} K (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (EuclideanDomain.instIsDomainToSemiringToRingToCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_2)) (Cubic.map.{u1, u2} F K (DivisionSemiring.toSemiring.{u1} F (Semifield.toDivisionSemiring.{u1} F (Field.toSemifield.{u1} F _inst_1))) (DivisionSemiring.toSemiring.{u2} K (Semifield.toDivisionSemiring.{u2} K (Field.toSemifield.{u2} K _inst_2))) φ P)))) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)))
+Case conversion may be inaccurate. Consider using '#align cubic.card_roots_of_disc_ne_zero Cubic.card_roots_of_disc_ne_zeroₓ'. -/
 theorem card_roots_of_disc_ne_zero [DecidableEq K] (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
     (hd : P.disc ≠ 0) : (map φ P).roots.toFinset.card = 3 :=
   by

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

@@ -141,7 +141,7 @@ theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
 #align cubic.to_poly_injective Cubic.toPoly_injective
 
 theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
-  rw [to_poly, ha, C_0, zero_mul, zero_add]
+  rw [to_poly, ha, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_a_eq_zero Cubic.of_a_eq_zero
 
 theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
@@ -149,7 +149,7 @@ theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
 #align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'
 
 theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.d := by
-  rw [of_a_eq_zero ha, hb, C_0, zero_mul, zero_add]
+  rw [of_a_eq_zero ha, hb, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_b_eq_zero Cubic.of_b_eq_zero
 
 theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
@@ -157,7 +157,7 @@ theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
 #align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'
 
 theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C P.d := by
-  rw [of_b_eq_zero ha hb, hc, C_0, zero_mul, zero_add]
+  rw [of_b_eq_zero ha hb, hc, C_0, MulZeroClass.zero_mul, zero_add]
 #align cubic.of_c_eq_zero Cubic.of_c_eq_zero
 
 theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = C d :=

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

@@ -64,11 +64,11 @@ variable {P Q : Cubic R} {a b c d a' b' c' d' : R} [Semiring R]
 
 /-- Convert a cubic polynomial to a polynomial. -/
 def toPoly (P : Cubic R) : R[X] :=
-  c P.a * x ^ 3 + c P.b * x ^ 2 + c P.c * x + c P.d
+  C P.a * X ^ 3 + C P.b * X ^ 2 + C P.c * X + C P.d
 #align cubic.to_poly Cubic.toPoly
 
 theorem c_mul_prod_x_sub_c_eq [CommRing S] {w x y z : S} :
-    c w * (x - c x) * (x - c y) * (x - c z) =
+    C w * (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨w, w * -(x + y + z), w * (x * y + x * z + y * z), w * -(x * y * z)⟩ :=
   by
   simp only [to_poly, C_neg, C_add, C_mul]
@@ -76,7 +76,7 @@ theorem c_mul_prod_x_sub_c_eq [CommRing S] {w x y z : S} :
 #align cubic.C_mul_prod_X_sub_C_eq Cubic.c_mul_prod_x_sub_c_eq
 
 theorem prod_x_sub_c_eq [CommRing S] {x y z : S} :
-    (x - c x) * (x - c y) * (x - c z) =
+    (X - C x) * (X - C y) * (X - C z) =
       toPoly ⟨1, -(x + y + z), x * y + x * z + y * z, -(x * y * z)⟩ :=
   by rw [← one_mul <| X - C x, ← C_1, C_mul_prod_X_sub_C_eq, one_mul, one_mul, one_mul]
 #align cubic.prod_X_sub_C_eq Cubic.prod_x_sub_c_eq
@@ -140,27 +140,27 @@ theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
   ⟨fun h => ext P Q (a_of_eq h) (b_of_eq h) (c_of_eq h) (d_of_eq h), congr_arg toPoly⟩
 #align cubic.to_poly_injective Cubic.toPoly_injective
 
-theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = c P.b * x ^ 2 + c P.c * x + c P.d := by
+theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
   rw [to_poly, ha, C_0, zero_mul, zero_add]
 #align cubic.of_a_eq_zero Cubic.of_a_eq_zero
 
-theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = c b * x ^ 2 + c c * x + c d :=
+theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
   of_a_eq_zero rfl
 #align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'
 
-theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = c P.c * x + c P.d := by
+theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.d := by
   rw [of_a_eq_zero ha, hb, C_0, zero_mul, zero_add]
 #align cubic.of_b_eq_zero Cubic.of_b_eq_zero
 
-theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = c c * x + c d :=
+theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
   of_b_eq_zero rfl rfl
 #align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'
 
-theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = c P.d := by
+theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C P.d := by
   rw [of_b_eq_zero ha hb, hc, C_0, zero_mul, zero_add]
 #align cubic.of_c_eq_zero Cubic.of_c_eq_zero
 
-theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = c d :=
+theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = C d :=
   of_c_eq_zero rfl rfl rfl
 #align cubic.of_c_eq_zero' Cubic.of_c_eq_zero'
 
@@ -538,7 +538,7 @@ theorem splits_iff_roots_eq_three (ha : P.a ≠ 0) :
 #align cubic.splits_iff_roots_eq_three Cubic.splits_iff_roots_eq_three
 
 theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
-    (map φ P).toPoly = c (φ P.a) * (x - c x) * (x - c y) * (x - c z) :=
+    (map φ P).toPoly = C (φ P.a) * (X - C x) * (X - C y) * (X - C z) :=
   by
   rw [map_to_poly,
     eq_prod_roots_of_splits <|

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

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Kurniadi Angdinata
 -/
-import Mathlib.Data.Polynomial.Splits
+import Mathlib.Algebra.Polynomial.Splits
 
 #align_import algebra.cubic_discriminant from "leanprover-community/mathlib"@"930133160e24036d5242039fe4972407cd4f1222"
 

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -87,7 +87,7 @@ section Coeff
 private theorem coeffs : (∀ n > 3, P.toPoly.coeff n = 0) ∧ P.toPoly.coeff 3 = P.a ∧
     P.toPoly.coeff 2 = P.b ∧ P.toPoly.coeff 1 = P.c ∧ P.toPoly.coeff 0 = P.d := by
   simp only [toPoly, coeff_add, coeff_C, coeff_C_mul_X, coeff_C_mul_X_pow]
-  norm_num
+  set_option tactic.skipAssignedInstances false in norm_num
   intro n hn
   repeat' rw [if_neg]
   any_goals linarith only [hn]

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

@@ -233,7 +233,7 @@ theorem leadingCoeff_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
   rw [of_c_eq_zero ha hb hc, leadingCoeff_C]
 #align cubic.leading_coeff_of_c_eq_zero Cubic.leadingCoeff_of_c_eq_zero
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- porting note (#10618): simp can prove this
 theorem leadingCoeff_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).leadingCoeff = d :=
   leadingCoeff_of_c_eq_zero rfl rfl rfl
 #align cubic.leading_coeff_of_c_eq_zero' Cubic.leadingCoeff_of_c_eq_zero'
@@ -368,7 +368,7 @@ theorem degree_of_d_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) (hd : P
   rw [of_d_eq_zero ha hb hc hd, degree_zero]
 #align cubic.degree_of_d_eq_zero Cubic.degree_of_d_eq_zero
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- porting note (#10618): simp can prove this
 theorem degree_of_d_eq_zero' : (⟨0, 0, 0, 0⟩ : Cubic R).toPoly.degree = ⊥ :=
   degree_of_d_eq_zero rfl rfl rfl rfl
 #align cubic.degree_of_d_eq_zero' Cubic.degree_of_d_eq_zero'
@@ -431,7 +431,7 @@ theorem natDegree_of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) :
   rw [of_c_eq_zero ha hb hc, natDegree_C]
 #align cubic.nat_degree_of_c_eq_zero Cubic.natDegree_of_c_eq_zero
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- porting note (#10618): simp can prove this
 theorem natDegree_of_c_eq_zero' : (toPoly ⟨0, 0, 0, d⟩).natDegree = 0 :=
   natDegree_of_c_eq_zero rfl rfl rfl
 #align cubic.nat_degree_of_c_eq_zero' Cubic.natDegree_of_c_eq_zero'

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).

@@ -135,7 +135,7 @@ theorem toPoly_injective (P Q : Cubic R) : P.toPoly = Q.toPoly ↔ P = Q :=
 #align cubic.to_poly_injective Cubic.toPoly_injective
 
 theorem of_a_eq_zero (ha : P.a = 0) : P.toPoly = C P.b * X ^ 2 + C P.c * X + C P.d := by
-  rw [toPoly, ha, C_0, MulZeroClass.zero_mul, zero_add]
+  rw [toPoly, ha, C_0, zero_mul, zero_add]
 #align cubic.of_a_eq_zero Cubic.of_a_eq_zero
 
 theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
@@ -143,7 +143,7 @@ theorem of_a_eq_zero' : toPoly ⟨0, b, c, d⟩ = C b * X ^ 2 + C c * X + C d :=
 #align cubic.of_a_eq_zero' Cubic.of_a_eq_zero'
 
 theorem of_b_eq_zero (ha : P.a = 0) (hb : P.b = 0) : P.toPoly = C P.c * X + C P.d := by
-  rw [of_a_eq_zero ha, hb, C_0, MulZeroClass.zero_mul, zero_add]
+  rw [of_a_eq_zero ha, hb, C_0, zero_mul, zero_add]
 #align cubic.of_b_eq_zero Cubic.of_b_eq_zero
 
 theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
@@ -151,7 +151,7 @@ theorem of_b_eq_zero' : toPoly ⟨0, 0, c, d⟩ = C c * X + C d :=
 #align cubic.of_b_eq_zero' Cubic.of_b_eq_zero'
 
 theorem of_c_eq_zero (ha : P.a = 0) (hb : P.b = 0) (hc : P.c = 0) : P.toPoly = C P.d := by
-  rw [of_b_eq_zero ha hb, hc, C_0, MulZeroClass.zero_mul, zero_add]
+  rw [of_b_eq_zero ha hb, hc, C_0, zero_mul, zero_add]
 #align cubic.of_c_eq_zero Cubic.of_c_eq_zero
 
 theorem of_c_eq_zero' : toPoly ⟨0, 0, 0, d⟩ = C d :=

The major change here is adapting to simp failing if it makes no progress. The vast majority of the redundant simps found due to this change were extracted to #6632.

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

@@ -291,7 +291,7 @@ def equiv : Cubic R ≃ { p : R[X] // p.degree ≤ 3 } where
     -- Porting note: Added `simp only [Nat.zero_eq, Nat.succ_eq_add_one] <;> ring_nf`
     -- There's probably a better way to do this.
     ext (_ | _ | _ | _ | n) <;> simp only [Nat.zero_eq, Nat.succ_eq_add_one] <;> ring_nf
-      <;> simp only [coeffs]
+      <;> try simp only [coeffs]
     have h3 : 3 < 4 + n := by linarith only
     rw [coeff_eq_zero h3,
       (degree_le_iff_coeff_zero (f : R[X]) 3).mp f.2 _ <| WithBot.coe_lt_coe.mpr (by exact h3)]

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

This has nice performance benefits.

@@ -37,7 +37,7 @@ noncomputable section
 
 /-- The structure representing a cubic polynomial. -/
 @[ext]
-structure Cubic (R : Type _) where
+structure Cubic (R : Type*) where
   (a b c d : R)
 #align cubic Cubic
 
@@ -47,7 +47,7 @@ open Cubic Polynomial
 
 open Polynomial
 
-variable {R S F K : Type _}
+variable {R S F K : Type*}
 
 instance [Inhabited R] : Inhabited (Cubic R) :=
   ⟨⟨default, default, default, default⟩⟩
@@ -559,7 +559,7 @@ end Split
 section Discriminant
 
 /-- The discriminant of a cubic polynomial. -/
-def disc {R : Type _} [Ring R] (P : Cubic R) : R :=
+def disc {R : Type*} [Ring R] (P : Cubic R) : R :=
   P.b ^ 2 * P.c ^ 2 - 4 * P.a * P.c ^ 3 - 4 * P.b ^ 3 * P.d - 27 * P.a ^ 2 * P.d ^ 2 +
     18 * P.a * P.b * P.c * P.d
 #align cubic.disc Cubic.disc

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 David Kurniadi Angdinata. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Kurniadi Angdinata
-
-! This file was ported from Lean 3 source module algebra.cubic_discriminant
-! leanprover-community/mathlib commit 930133160e24036d5242039fe4972407cd4f1222
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.Splits
 
+#align_import algebra.cubic_discriminant from "leanprover-community/mathlib"@"930133160e24036d5242039fe4972407cd4f1222"
+
 /-!
 # Cubics and discriminants
 

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>

@@ -531,8 +531,6 @@ theorem eq_prod_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z})
   rw [prod_cons, prod_cons, prod_singleton, mul_assoc, mul_assoc]
 #align cubic.eq_prod_three_roots Cubic.eq_prod_three_roots
 
--- Porting note: Increased heartbeat limit for `C_mul_prod_X_sub_C_eq`
-set_option maxHeartbeats 500000 in
 theorem eq_sum_three_roots (ha : P.a ≠ 0) (h3 : (map φ P).roots = {x, y, z}) :
     map φ P =
       ⟨φ P.a, φ P.a * -(x + y + z), φ P.a * (x * y + x * z + y * z), φ P.a * -(x * y * z)⟩ := by