data.polynomial.hasse_deriv | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

a148d797

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

10bf4f82

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -6,7 +6,7 @@ Authors: Johan Commelin
 import Algebra.Polynomial.BigOperators
 import Data.Nat.Choose.Cast
 import Data.Nat.Choose.Vandermonde
-import Data.Polynomial.Derivative
+import Algebra.Polynomial.Derivative
 
 #align_import data.polynomial.hasse_deriv from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -78,7 +78,7 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
     rw [coeff_monomial]
     by_cases hik : i < k
     · simp only [Nat.choose_eq_zero_of_lt hik, if_t_t, Nat.cast_zero, MulZeroClass.zero_mul]
-    · push_neg at hik ; rw [if_neg]; contrapose! hink
+    · push_neg at hik; rw [if_neg]; contrapose! hink
       exact (tsub_eq_iff_eq_add_of_le hik).mp hink
   · intro h;
     simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
@@ -133,8 +133,8 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
   · rw [if_pos hnik, if_pos, ← hnik]; apply tsub_eq_of_eq_add_rev; rwa [add_comm]
   · rw [if_neg hnik, MulZeroClass.mul_zero]
     by_cases hkn : k ≤ n
-    · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik ; rw [if_neg hnik]
-    · push_neg at hkn ;
+    · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik; rw [if_neg hnik]
+    · push_neg at hkn;
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 -/
@@ -200,9 +200,9 @@ theorem hasseDeriv_comp (k l : ℕ) :
   · rw [choose_eq_zero_of_lt hikl, MulZeroClass.mul_zero]
     by_cases hil : i < l
     · rw [choose_eq_zero_of_lt hil, MulZeroClass.mul_zero]
-    · push_neg at hil ; rw [← tsub_lt_iff_right hil] at hikl 
+    · push_neg at hil; rw [← tsub_lt_iff_right hil] at hikl
       rw [choose_eq_zero_of_lt hikl, MulZeroClass.zero_mul]
-  push_neg at hikl ; apply @cast_injective ℚ
+  push_neg at hikl; apply @cast_injective ℚ
   have h1 : l ≤ i := le_of_add_le_right hikl
   have h2 : k ≤ i - l := le_tsub_of_add_le_right hikl
   have h3 : k ≤ k + l := le_self_add
@@ -250,7 +250,7 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
       simp only [ite_eq_right_iff, Ne.def, nat_degree_monomial, hasse_deriv_monomial]
       intro k c c0 hh
       -- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
-      rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh 
+      rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh
       exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
 #align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDeriv
 -/
@@ -279,7 +279,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
         monomial (m - x.1 + (n - x.2)) (↑(m.choose x.1) * r * (↑(n.choose x.2) * s)) =
           monomial (m + n - k) (↑(m.choose x.1) * ↑(n.choose x.2) * (r * s)) :=
     by
-    intro x hx; rw [Finset.Nat.mem_antidiagonal] at hx ; subst hx
+    intro x hx; rw [Finset.Nat.mem_antidiagonal] at hx; subst hx
     by_cases hm : m < x.1
     ·
       simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, MulZeroClass.zero_mul,
@@ -288,7 +288,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     ·
       simp only [Nat.choose_eq_zero_of_lt hn, Nat.cast_zero, MulZeroClass.zero_mul,
         MulZeroClass.mul_zero, monomial_zero_right]
-    push_neg at hm hn 
+    push_neg at hm hn
     rw [tsub_add_eq_add_tsub hm, ← add_tsub_assoc_of_le hn, ← tsub_add_eq_tsub_tsub,
       add_comm x.2 x.1, mul_assoc, ← mul_assoc r, ← (Nat.cast_commute _ r).Eq, mul_assoc, mul_assoc]
   conv_rhs =>

10bf4f82

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -219,7 +219,21 @@ theorem hasseDeriv_comp (k l : ℕ) :
 
 #print Polynomial.natDegree_hasseDeriv_le /-
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
-  by classical
+  by
+  classical
+  rw [hasse_deriv_apply, sum_def]
+  refine' (nat_degree_sum_le _ _).trans _
+  simp_rw [Function.comp, nat_degree_monomial]
+  rw [Finset.fold_ite, Finset.fold_const]
+  · simp only [if_t_t, max_eq_right, zero_le', Finset.fold_max_le, true_and_iff, and_imp,
+      tsub_le_iff_right, mem_support_iff, Ne.def, Finset.mem_filter]
+    intro x hx hx'
+    have hxp : x ≤ p.nat_degree := le_nat_degree_of_ne_zero hx
+    have hxn : n ≤ x := by
+      contrapose! hx'
+      simp [Nat.choose_eq_zero_of_lt hx']
+    rwa [tsub_add_cancel_of_le (hxn.trans hxp)]
+  · simp
 #align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_le
 -/
 
@@ -231,11 +245,16 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
   · simpa [hasse_deriv_eq_zero_of_lt_nat_degree, hn] using (tsub_eq_zero_of_le hn.le).symm
   · refine' map_nat_degree_eq_sub _ _
     · exact fun h => hasse_deriv_eq_zero_of_lt_nat_degree _ _
-    · classical
+    ·
+      classical
+      simp only [ite_eq_right_iff, Ne.def, nat_degree_monomial, hasse_deriv_monomial]
+      intro k c c0 hh
+      -- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
+      rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh 
+      exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
 #align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDeriv
 -/
 
--- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
 section
 
 open AddMonoidHom Finset.Nat

10bf4f82

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -219,21 +219,7 @@ theorem hasseDeriv_comp (k l : ℕ) :
 
 #print Polynomial.natDegree_hasseDeriv_le /-
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
-  by
-  classical
-  rw [hasse_deriv_apply, sum_def]
-  refine' (nat_degree_sum_le _ _).trans _
-  simp_rw [Function.comp, nat_degree_monomial]
-  rw [Finset.fold_ite, Finset.fold_const]
-  · simp only [if_t_t, max_eq_right, zero_le', Finset.fold_max_le, true_and_iff, and_imp,
-      tsub_le_iff_right, mem_support_iff, Ne.def, Finset.mem_filter]
-    intro x hx hx'
-    have hxp : x ≤ p.nat_degree := le_nat_degree_of_ne_zero hx
-    have hxn : n ≤ x := by
-      contrapose! hx'
-      simp [Nat.choose_eq_zero_of_lt hx']
-    rwa [tsub_add_cancel_of_le (hxn.trans hxp)]
-  · simp
+  by classical
 #align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_le
 -/
 
@@ -245,16 +231,11 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
   · simpa [hasse_deriv_eq_zero_of_lt_nat_degree, hn] using (tsub_eq_zero_of_le hn.le).symm
   · refine' map_nat_degree_eq_sub _ _
     · exact fun h => hasse_deriv_eq_zero_of_lt_nat_degree _ _
-    ·
-      classical
-      simp only [ite_eq_right_iff, Ne.def, nat_degree_monomial, hasse_deriv_monomial]
-      intro k c c0 hh
-      -- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
-      rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh 
-      exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
+    · classical
 #align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDeriv
 -/
 
+-- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
 section
 
 open AddMonoidHom Finset.Nat

10bf4f82

bump to nightly-2023-10-04-06

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

7bd6a14d

Diff

@@ -295,7 +295,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     apply_congr
     skip
     rw [aux _ H]
-  rw_mod_cast [← LinearMap.map_sum, ← Finset.sum_mul, ← Nat.add_choose_eq]
+  rw_mod_cast [← map_sum, ← Finset.sum_mul, ← Nat.add_choose_eq]
 #align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mul
 -/

10bf4f82

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.Algebra.Polynomial.BigOperators
-import Mathbin.Data.Nat.Choose.Cast
-import Mathbin.Data.Nat.Choose.Vandermonde
-import Mathbin.Data.Polynomial.Derivative
+import Algebra.Polynomial.BigOperators
+import Data.Nat.Choose.Cast
+import Data.Nat.Choose.Vandermonde
+import Data.Polynomial.Derivative
 
 #align_import data.polynomial.hasse_deriv from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.polynomial.hasse_deriv
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Polynomial.BigOperators
 import Mathbin.Data.Nat.Choose.Cast
 import Mathbin.Data.Nat.Choose.Vandermonde
 import Mathbin.Data.Polynomial.Derivative
 
+#align_import data.polynomial.hasse_deriv from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Hasse derivative of polynomials

10bf4f82

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -167,7 +167,7 @@ theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative
   by
   induction' k with k ih
   · rw [hasse_deriv_zero, factorial_zero, iterate_zero, one_smul, LinearMap.id_coe]
-  ext (f n) : 2
+  ext f n : 2
   rw [iterate_succ_apply', ← ih]
   simp only [LinearMap.smul_apply, coeff_smul, LinearMap.map_smul_of_tower, coeff_derivative,
     hasse_deriv_coeff, ← @choose_symm_add _ k]
@@ -273,7 +273,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
       ∑ ij : ℕ × ℕ in antidiagonal k, ((comp_hom.comp ((comp_hom Φ) (D ij.1))).flip (D ij.2) f) g
   simp only [← finset_sum_apply]
   congr 2; clear f g
-  ext (m r n s) : 4
+  ext m r n s : 4
   simp only [finset_sum_apply, coe_mul_left, coe_comp, flip_apply, comp_app, hasse_deriv_monomial,
     LinearMap.toAddMonoidHom_coe, comp_hom_apply_apply, coe_mul, monomial_mul_monomial]
   have aux :

10bf4f82

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -66,10 +66,13 @@ def hasseDeriv (k : ℕ) : R[X] →ₗ[R] R[X] :=
 #align polynomial.hasse_deriv Polynomial.hasseDeriv
 -/
 
+#print Polynomial.hasseDeriv_apply /-
 theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (↑(i.choose k) * r) :=
   by simpa only [← nsmul_eq_mul]
 #align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_apply
+-/
 
+#print Polynomial.hasseDeriv_coeff /-
 theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) :=
   by
   rw [hasse_deriv_apply, coeff_sum, sum_def, Finset.sum_eq_single (n + k), coeff_monomial]
@@ -83,11 +86,14 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
   · intro h;
     simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
 #align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeff
+-/
 
+#print Polynomial.hasseDeriv_zero' /-
 theorem hasseDeriv_zero' : hasseDeriv 0 f = f := by
   simp only [hasse_deriv_apply, tsub_zero, Nat.choose_zero_right, Nat.cast_one, one_mul,
     sum_monomial_eq]
 #align polynomial.hasse_deriv_zero' Polynomial.hasseDeriv_zero'
+-/
 
 #print Polynomial.hasseDeriv_zero /-
 @[simp]
@@ -96,17 +102,21 @@ theorem hasseDeriv_zero : @hasseDeriv R _ 0 = LinearMap.id :=
 #align polynomial.hasse_deriv_zero Polynomial.hasseDeriv_zero
 -/
 
+#print Polynomial.hasseDeriv_eq_zero_of_lt_natDegree /-
 theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree < n) :
     hasseDeriv n p = 0 := by
   rw [hasse_deriv_apply, sum_def]
   refine' Finset.sum_eq_zero fun x hx => _
   simp [Nat.choose_eq_zero_of_lt ((le_nat_degree_of_mem_supp _ hx).trans_lt h)]
 #align polynomial.hasse_deriv_eq_zero_of_lt_nat_degree Polynomial.hasseDeriv_eq_zero_of_lt_natDegree
+-/
 
+#print Polynomial.hasseDeriv_one' /-
 theorem hasseDeriv_one' : hasseDeriv 1 f = derivative f := by
   simp only [hasse_deriv_apply, derivative_apply, ← C_mul_X_pow_eq_monomial, Nat.choose_one_right,
     (Nat.cast_commute _ _).Eq]
 #align polynomial.hasse_deriv_one' Polynomial.hasseDeriv_one'
+-/
 
 #print Polynomial.hasseDeriv_one /-
 @[simp]
@@ -115,6 +125,7 @@ theorem hasseDeriv_one : @hasseDeriv R _ 1 = derivative :=
 #align polynomial.hasse_deriv_one Polynomial.hasseDeriv_one
 -/
 
+#print Polynomial.hasseDeriv_monomial /-
 @[simp]
 theorem hasseDeriv_monomial (n : ℕ) (r : R) :
     hasseDeriv k (monomial n r) = monomial (n - k) (↑(n.choose k) * r) :=
@@ -129,21 +140,29 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
     · push_neg at hkn ;
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
+-/
 
+#print Polynomial.hasseDeriv_C /-
 theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     MulZeroClass.zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_C Polynomial.hasseDeriv_C
+-/
 
+#print Polynomial.hasseDeriv_apply_one /-
 theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
   rw [← C_1, hasse_deriv_C k _ hk]
 #align polynomial.hasse_deriv_apply_one Polynomial.hasseDeriv_apply_one
+-/
 
+#print Polynomial.hasseDeriv_X /-
 theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     MulZeroClass.zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_X Polynomial.hasseDeriv_X
+-/
 
+#print Polynomial.factorial_smul_hasseDeriv /-
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] :=
   by
   induction' k with k ih
@@ -168,6 +187,7 @@ theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative
   norm_cast
   simp only [factorial_succ, succ_eq_add_one]; ring
 #align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDeriv
+-/
 
 #print Polynomial.hasseDeriv_comp /-
 theorem hasseDeriv_comp (k l : ℕ) :
@@ -200,6 +220,7 @@ theorem hasseDeriv_comp (k l : ℕ) :
 #align polynomial.hasse_deriv_comp Polynomial.hasseDeriv_comp
 -/
 
+#print Polynomial.natDegree_hasseDeriv_le /-
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
   by
   classical
@@ -217,7 +238,9 @@ theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p
     rwa [tsub_add_cancel_of_le (hxn.trans hxp)]
   · simp
 #align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_le
+-/
 
+#print Polynomial.natDegree_hasseDeriv /-
 theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
     natDegree (hasseDeriv n p) = natDegree p - n :=
   by
@@ -233,11 +256,13 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
       rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh 
       exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
 #align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDeriv
+-/
 
 section
 
 open AddMonoidHom Finset.Nat
 
+#print Polynomial.hasseDeriv_mul /-
 theorem hasseDeriv_mul (f g : R[X]) :
     hasseDeriv k (f * g) = ∑ ij in antidiagonal k, hasseDeriv ij.1 f * hasseDeriv ij.2 g :=
   by
@@ -275,6 +300,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     rw [aux _ H]
   rw_mod_cast [← LinearMap.map_sum, ← Finset.sum_mul, ← Nat.add_choose_eq]
 #align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mul
+-/
 
 end

10bf4f82

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -78,7 +78,7 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
     rw [coeff_monomial]
     by_cases hik : i < k
     · simp only [Nat.choose_eq_zero_of_lt hik, if_t_t, Nat.cast_zero, MulZeroClass.zero_mul]
-    · push_neg  at hik ; rw [if_neg]; contrapose! hink
+    · push_neg at hik ; rw [if_neg]; contrapose! hink
       exact (tsub_eq_iff_eq_add_of_le hik).mp hink
   · intro h;
     simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
@@ -126,7 +126,7 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
   · rw [if_neg hnik, MulZeroClass.mul_zero]
     by_cases hkn : k ≤ n
     · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik ; rw [if_neg hnik]
-    · push_neg  at hkn ;
+    · push_neg at hkn ;
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
@@ -183,9 +183,9 @@ theorem hasseDeriv_comp (k l : ℕ) :
   · rw [choose_eq_zero_of_lt hikl, MulZeroClass.mul_zero]
     by_cases hil : i < l
     · rw [choose_eq_zero_of_lt hil, MulZeroClass.mul_zero]
-    · push_neg  at hil ; rw [← tsub_lt_iff_right hil] at hikl 
+    · push_neg at hil ; rw [← tsub_lt_iff_right hil] at hikl 
       rw [choose_eq_zero_of_lt hikl, MulZeroClass.zero_mul]
-  push_neg  at hikl ; apply @cast_injective ℚ
+  push_neg at hikl ; apply @cast_injective ℚ
   have h1 : l ≤ i := le_of_add_le_right hikl
   have h2 : k ≤ i - l := le_tsub_of_add_le_right hikl
   have h3 : k ≤ k + l := le_self_add
@@ -203,19 +203,19 @@ theorem hasseDeriv_comp (k l : ℕ) :
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
   by
   classical
-    rw [hasse_deriv_apply, sum_def]
-    refine' (nat_degree_sum_le _ _).trans _
-    simp_rw [Function.comp, nat_degree_monomial]
-    rw [Finset.fold_ite, Finset.fold_const]
-    · simp only [if_t_t, max_eq_right, zero_le', Finset.fold_max_le, true_and_iff, and_imp,
-        tsub_le_iff_right, mem_support_iff, Ne.def, Finset.mem_filter]
-      intro x hx hx'
-      have hxp : x ≤ p.nat_degree := le_nat_degree_of_ne_zero hx
-      have hxn : n ≤ x := by
-        contrapose! hx'
-        simp [Nat.choose_eq_zero_of_lt hx']
-      rwa [tsub_add_cancel_of_le (hxn.trans hxp)]
-    · simp
+  rw [hasse_deriv_apply, sum_def]
+  refine' (nat_degree_sum_le _ _).trans _
+  simp_rw [Function.comp, nat_degree_monomial]
+  rw [Finset.fold_ite, Finset.fold_const]
+  · simp only [if_t_t, max_eq_right, zero_le', Finset.fold_max_le, true_and_iff, and_imp,
+      tsub_le_iff_right, mem_support_iff, Ne.def, Finset.mem_filter]
+    intro x hx hx'
+    have hxp : x ≤ p.nat_degree := le_nat_degree_of_ne_zero hx
+    have hxn : n ≤ x := by
+      contrapose! hx'
+      simp [Nat.choose_eq_zero_of_lt hx']
+    rwa [tsub_add_cancel_of_le (hxn.trans hxp)]
+  · simp
 #align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_le
 
 theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
@@ -227,11 +227,11 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
     · exact fun h => hasse_deriv_eq_zero_of_lt_nat_degree _ _
     ·
       classical
-        simp only [ite_eq_right_iff, Ne.def, nat_degree_monomial, hasse_deriv_monomial]
-        intro k c c0 hh
-        -- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
-        rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh 
-        exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
+      simp only [ite_eq_right_iff, Ne.def, nat_degree_monomial, hasse_deriv_monomial]
+      intro k c c0 hh
+      -- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
+      rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh 
+      exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
 #align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDeriv
 
 section
@@ -266,7 +266,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     ·
       simp only [Nat.choose_eq_zero_of_lt hn, Nat.cast_zero, MulZeroClass.zero_mul,
         MulZeroClass.mul_zero, monomial_zero_right]
-    push_neg  at hm hn 
+    push_neg at hm hn 
     rw [tsub_add_eq_add_tsub hm, ← add_tsub_assoc_of_le hn, ← tsub_add_eq_tsub_tsub,
       add_comm x.2 x.1, mul_assoc, ← mul_assoc r, ← (Nat.cast_commute _ r).Eq, mul_assoc, mul_assoc]
   conv_rhs =>

10bf4f82

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -78,7 +78,7 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
     rw [coeff_monomial]
     by_cases hik : i < k
     · simp only [Nat.choose_eq_zero_of_lt hik, if_t_t, Nat.cast_zero, MulZeroClass.zero_mul]
-    · push_neg  at hik; rw [if_neg]; contrapose! hink
+    · push_neg  at hik ; rw [if_neg]; contrapose! hink
       exact (tsub_eq_iff_eq_add_of_le hik).mp hink
   · intro h;
     simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
@@ -125,8 +125,8 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
   · rw [if_pos hnik, if_pos, ← hnik]; apply tsub_eq_of_eq_add_rev; rwa [add_comm]
   · rw [if_neg hnik, MulZeroClass.mul_zero]
     by_cases hkn : k ≤ n
-    · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik; rw [if_neg hnik]
-    · push_neg  at hkn;
+    · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik ; rw [if_neg hnik]
+    · push_neg  at hkn ;
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
@@ -183,9 +183,9 @@ theorem hasseDeriv_comp (k l : ℕ) :
   · rw [choose_eq_zero_of_lt hikl, MulZeroClass.mul_zero]
     by_cases hil : i < l
     · rw [choose_eq_zero_of_lt hil, MulZeroClass.mul_zero]
-    · push_neg  at hil; rw [← tsub_lt_iff_right hil] at hikl
+    · push_neg  at hil ; rw [← tsub_lt_iff_right hil] at hikl 
       rw [choose_eq_zero_of_lt hikl, MulZeroClass.zero_mul]
-  push_neg  at hikl; apply @cast_injective ℚ
+  push_neg  at hikl ; apply @cast_injective ℚ
   have h1 : l ≤ i := le_of_add_le_right hikl
   have h2 : k ≤ i - l := le_tsub_of_add_le_right hikl
   have h3 : k ≤ k + l := le_self_add
@@ -230,7 +230,7 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
         simp only [ite_eq_right_iff, Ne.def, nat_degree_monomial, hasse_deriv_monomial]
         intro k c c0 hh
         -- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
-        rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh
+        rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh 
         exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
 #align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDeriv
 
@@ -257,7 +257,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
         monomial (m - x.1 + (n - x.2)) (↑(m.choose x.1) * r * (↑(n.choose x.2) * s)) =
           monomial (m + n - k) (↑(m.choose x.1) * ↑(n.choose x.2) * (r * s)) :=
     by
-    intro x hx; rw [Finset.Nat.mem_antidiagonal] at hx; subst hx
+    intro x hx; rw [Finset.Nat.mem_antidiagonal] at hx ; subst hx
     by_cases hm : m < x.1
     ·
       simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, MulZeroClass.zero_mul,
@@ -266,7 +266,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     ·
       simp only [Nat.choose_eq_zero_of_lt hn, Nat.cast_zero, MulZeroClass.zero_mul,
         MulZeroClass.mul_zero, monomial_zero_right]
-    push_neg  at hm hn
+    push_neg  at hm hn 
     rw [tsub_add_eq_add_tsub hm, ← add_tsub_assoc_of_le hn, ← tsub_add_eq_tsub_tsub,
       add_comm x.2 x.1, mul_assoc, ← mul_assoc r, ← (Nat.cast_commute _ r).Eq, mul_assoc, mul_assoc]
   conv_rhs =>

10bf4f82

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -50,7 +50,7 @@ noncomputable section
 
 namespace Polynomial
 
-open Nat BigOperators Polynomial
+open scoped Nat BigOperators Polynomial
 
 open Function

10bf4f82

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -66,19 +66,10 @@ def hasseDeriv (k : ℕ) : R[X] →ₗ[R] R[X] :=
 #align polynomial.hasse_deriv Polynomial.hasseDeriv
 -/
 
-/- warning: polynomial.hasse_deriv_apply -> Polynomial.hasseDeriv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_applyₓ'. -/
 theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (↑(i.choose k) * r) :=
   by simpa only [← nsmul_eq_mul]
 #align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_apply
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeffₓ'. -/
 theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) :=
   by
   rw [hasse_deriv_apply, coeff_sum, sum_def, Finset.sum_eq_single (n + k), coeff_monomial]
@@ -93,12 +84,6 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
     simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
 #align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeff
 
-/- warning: polynomial.hasse_deriv_zero' -> Polynomial.hasseDeriv_zero' is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_zero' Polynomial.hasseDeriv_zero'ₓ'. -/
 theorem hasseDeriv_zero' : hasseDeriv 0 f = f := by
   simp only [hasse_deriv_apply, tsub_zero, Nat.choose_zero_right, Nat.cast_one, one_mul,
     sum_monomial_eq]
@@ -111,12 +96,6 @@ theorem hasseDeriv_zero : @hasseDeriv R _ 0 = LinearMap.id :=
 #align polynomial.hasse_deriv_zero Polynomial.hasseDeriv_zero
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_eq_zero_of_lt_nat_degree Polynomial.hasseDeriv_eq_zero_of_lt_natDegreeₓ'. -/
 theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree < n) :
     hasseDeriv n p = 0 := by
   rw [hasse_deriv_apply, sum_def]
@@ -124,12 +103,6 @@ theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree
   simp [Nat.choose_eq_zero_of_lt ((le_nat_degree_of_mem_supp _ hx).trans_lt h)]
 #align polynomial.hasse_deriv_eq_zero_of_lt_nat_degree Polynomial.hasseDeriv_eq_zero_of_lt_natDegree
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_one' Polynomial.hasseDeriv_one'ₓ'. -/
 theorem hasseDeriv_one' : hasseDeriv 1 f = derivative f := by
   simp only [hasse_deriv_apply, derivative_apply, ← C_mul_X_pow_eq_monomial, Nat.choose_one_right,
     (Nat.cast_commute _ _).Eq]
@@ -142,9 +115,6 @@ theorem hasseDeriv_one : @hasseDeriv R _ 1 = derivative :=
 #align polynomial.hasse_deriv_one Polynomial.hasseDeriv_one
 -/
 
-/- warning: polynomial.hasse_deriv_monomial -> Polynomial.hasseDeriv_monomial is a dubious translation:
-<too large>
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 @[simp]
 theorem hasseDeriv_monomial (n : ℕ) (r : R) :
     hasseDeriv k (monomial n r) = monomial (n - k) (↑(n.choose k) * r) :=
@@ -160,38 +130,20 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
-/- warning: polynomial.hasse_deriv_C -> Polynomial.hasseDeriv_C is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_Cₓ'. -/
 theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     MulZeroClass.zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_C Polynomial.hasseDeriv_C
 
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 theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
   rw [← C_1, hasse_deriv_C k _ hk]
 #align polynomial.hasse_deriv_apply_one Polynomial.hasseDeriv_apply_one
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_X Polynomial.hasseDeriv_Xₓ'. -/
 theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     MulZeroClass.zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_X Polynomial.hasseDeriv_X
 
-/- warning: polynomial.factorial_smul_hasse_deriv -> Polynomial.factorial_smul_hasseDeriv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDerivₓ'. -/
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] :=
   by
   induction' k with k ih
@@ -248,12 +200,6 @@ theorem hasseDeriv_comp (k l : ℕ) :
 #align polynomial.hasse_deriv_comp Polynomial.hasseDeriv_comp
 -/
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_leₓ'. -/
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
   by
   classical
@@ -272,12 +218,6 @@ theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p
     · simp
 #align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_le
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDerivₓ'. -/
 theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
     natDegree (hasseDeriv n p) = natDegree p - n :=
   by
@@ -298,9 +238,6 @@ section
 
 open AddMonoidHom Finset.Nat
 
-/- warning: polynomial.hasse_deriv_mul -> Polynomial.hasseDeriv_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mulₓ'. -/
 theorem hasseDeriv_mul (f g : R[X]) :
     hasseDeriv k (f * g) = ∑ ij in antidiagonal k, hasseDeriv ij.1 f * hasseDeriv ij.2 g :=
   by

10bf4f82

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -87,11 +87,9 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
     rw [coeff_monomial]
     by_cases hik : i < k
     · simp only [Nat.choose_eq_zero_of_lt hik, if_t_t, Nat.cast_zero, MulZeroClass.zero_mul]
-    · push_neg  at hik
-      rw [if_neg]
-      contrapose! hink
+    · push_neg  at hik; rw [if_neg]; contrapose! hink
       exact (tsub_eq_iff_eq_add_of_le hik).mp hink
-  · intro h
+  · intro h;
     simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
 #align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeff
 
@@ -154,14 +152,11 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
   ext i
   simp only [hasse_deriv_coeff, coeff_monomial]
   by_cases hnik : n = i + k
-  · rw [if_pos hnik, if_pos, ← hnik]
-    apply tsub_eq_of_eq_add_rev
-    rwa [add_comm]
+  · rw [if_pos hnik, if_pos, ← hnik]; apply tsub_eq_of_eq_add_rev; rwa [add_comm]
   · rw [if_neg hnik, MulZeroClass.mul_zero]
     by_cases hkn : k ≤ n
-    · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik
-      rw [if_neg hnik]
-    · push_neg  at hkn
+    · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik; rw [if_neg hnik]
+    · push_neg  at hkn;
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
@@ -208,9 +203,7 @@ theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative
   simp only [nsmul_eq_mul, factorial_succ, mul_assoc, succ_eq_add_one, ← add_assoc,
     add_right_comm n 1 k, ← cast_succ]
   rw [← (cast_commute (n + 1) (f.coeff (n + k + 1))).Eq]
-  simp only [← mul_assoc]
-  norm_cast
-  congr 2
+  simp only [← mul_assoc]; norm_cast; congr 2
   apply @cast_injective ℚ
   have h1 : n + 1 ≤ n + k + 1 := succ_le_succ le_self_add
   have h2 : k + 1 ≤ n + k + 1 := succ_le_succ le_add_self
@@ -221,8 +214,7 @@ theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative
   rw [eq_div_iff_mul_eq (mul_ne_zero (H _) (H _)), eq_comm, div_mul_eq_mul_div,
     eq_div_iff_mul_eq (mul_ne_zero (H _) (H _))]
   norm_cast
-  simp only [factorial_succ, succ_eq_add_one]
-  ring
+  simp only [factorial_succ, succ_eq_add_one]; ring
 #align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDeriv
 
 #print Polynomial.hasseDeriv_comp /-
@@ -239,11 +231,9 @@ theorem hasseDeriv_comp (k l : ℕ) :
   · rw [choose_eq_zero_of_lt hikl, MulZeroClass.mul_zero]
     by_cases hil : i < l
     · rw [choose_eq_zero_of_lt hil, MulZeroClass.mul_zero]
-    · push_neg  at hil
-      rw [← tsub_lt_iff_right hil] at hikl
+    · push_neg  at hil; rw [← tsub_lt_iff_right hil] at hikl
       rw [choose_eq_zero_of_lt hikl, MulZeroClass.zero_mul]
-  push_neg  at hikl
-  apply @cast_injective ℚ
+  push_neg  at hikl; apply @cast_injective ℚ
   have h1 : l ≤ i := le_of_add_le_right hikl
   have h2 : k ≤ i - l := le_tsub_of_add_le_right hikl
   have h3 : k ≤ k + l := le_self_add
@@ -320,8 +310,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     (comp_hom (D k)).comp Φ f g =
       ∑ ij : ℕ × ℕ in antidiagonal k, ((comp_hom.comp ((comp_hom Φ) (D ij.1))).flip (D ij.2) f) g
   simp only [← finset_sum_apply]
-  congr 2
-  clear f g
+  congr 2; clear f g
   ext (m r n s) : 4
   simp only [finset_sum_apply, coe_mul_left, coe_comp, flip_apply, comp_app, hasse_deriv_monomial,
     LinearMap.toAddMonoidHom_coe, comp_hom_apply_apply, coe_mul, monomial_mul_monomial]
@@ -331,9 +320,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
         monomial (m - x.1 + (n - x.2)) (↑(m.choose x.1) * r * (↑(n.choose x.2) * s)) =
           monomial (m + n - k) (↑(m.choose x.1) * ↑(n.choose x.2) * (r * s)) :=
     by
-    intro x hx
-    rw [Finset.Nat.mem_antidiagonal] at hx
-    subst hx
+    intro x hx; rw [Finset.Nat.mem_antidiagonal] at hx; subst hx
     by_cases hm : m < x.1
     ·
       simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, MulZeroClass.zero_mul,

10bf4f82

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -67,10 +67,7 @@ def hasseDeriv (k : ℕ) : R[X] →ₗ[R] R[X] :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_applyₓ'. -/
 theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (↑(i.choose k) * r) :=
   by simpa only [← nsmul_eq_mul]
@@ -148,10 +145,7 @@ theorem hasseDeriv_one : @hasseDeriv R _ 1 = derivative :=
 -/
 
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 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomialₓ'. -/
 @[simp]
 theorem hasseDeriv_monomial (n : ℕ) (r : R) :
@@ -172,10 +166,7 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
 /- warning: polynomial.hasse_deriv_C -> Polynomial.hasseDeriv_C is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_Cₓ'. -/
 theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
@@ -204,10 +195,7 @@ theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
 #align polynomial.hasse_deriv_X Polynomial.hasseDeriv_X
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDerivₓ'. -/
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] :=
   by
@@ -321,10 +309,7 @@ section
 open AddMonoidHom Finset.Nat
 
 /- warning: polynomial.hasse_deriv_mul -> Polynomial.hasseDeriv_mul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mulₓ'. -/
 theorem hasseDeriv_mul (f g : R[X]) :
     hasseDeriv k (f * g) = ∑ ij in antidiagonal k, hasseDeriv ij.1 f * hasseDeriv ij.2 g :=

10bf4f82

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -70,7 +70,7 @@ def hasseDeriv (k : ℕ) : R[X] →ₗ[R] R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) f (fun (i : Nat) (r : R) => coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Nat.choose i k)) r)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) f (fun (i : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose i k)) r)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) f (fun (i : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose i k)) r)))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_applyₓ'. -/
 theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (↑(i.choose k) * r) :=
   by simpa only [← nsmul_eq_mul]
@@ -80,7 +80,7 @@ theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) n) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k) k)) (Polynomial.coeff.{u1} R _inst_1 f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) n) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k) k)) (Polynomial.coeff.{u1} R _inst_1 f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) n) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k) k)) (Polynomial.coeff.{u1} R _inst_1 f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k)))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeffₓ'. -/
 theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) :=
   by
@@ -102,7 +102,7 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) f) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) f) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) f) f
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_zero' Polynomial.hasseDeriv_zero'ₓ'. -/
 theorem hasseDeriv_zero' : hasseDeriv 0 f = f := by
   simp only [hasse_deriv_apply, tsub_zero, Nat.choose_zero_right, Nat.cast_one, one_mul,
@@ -120,7 +120,7 @@ theorem hasseDeriv_zero : @hasseDeriv R _ 0 = LinearMap.id :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_eq_zero_of_lt_nat_degree Polynomial.hasseDeriv_eq_zero_of_lt_natDegreeₓ'. -/
 theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree < n) :
     hasseDeriv n p = 0 := by
@@ -133,7 +133,7 @@ theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) f) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1) f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_one' Polynomial.hasseDeriv_one'ₓ'. -/
 theorem hasseDeriv_one' : hasseDeriv 1 f = derivative f := by
   simp only [hasse_deriv_apply, derivative_apply, ← C_mul_X_pow_eq_monomial, Nat.choose_one_right,
@@ -151,7 +151,7 @@ theorem hasseDeriv_one : @hasseDeriv R _ 1 = derivative :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (n : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Nat.choose n k)) r))
 but is expected to have type
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Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose n k)) r))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (n : Nat) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose n k)) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomialₓ'. -/
 @[simp]
 theorem hasseDeriv_monomial (n : ℕ) (r : R) :
@@ -175,7 +175,7 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_Cₓ'. -/
 theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
@@ -186,7 +186,7 @@ theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 1 (One.one.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply_one Polynomial.hasseDeriv_apply_oneₓ'. -/
 theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
   rw [← C_1, hasse_deriv_C k _ hk]
@@ -196,7 +196,7 @@ theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (Polynomial.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (Polynomial.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (Polynomial.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_X Polynomial.hasseDeriv_Xₓ'. -/
 theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
@@ -207,7 +207,7 @@ theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), Eq.{succ u1} ((Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (SMul.smul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.hasSmul.{u1, u1, 0, u1, u1} R R Nat (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) Nat.monoid (Polynomial.distribMulAction.{u1, 0} R _inst_1 Nat Nat.monoid (Module.toDistribMulAction.{0, u1} Nat R Nat.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (AddCommMonoid.natModule.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Polynomial.smulCommClass.{u1, u1, 0} R _inst_1 R Nat (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Nat R Nat.hasZero (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddMonoid.natSMulWithZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (AddMonoid.nat_smulCommClass'.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), Eq.{succ u1} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HSMul.hSMul.{0, u1, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (instHSMul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoid.SMul.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Module.End.semiring.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), Eq.{succ u1} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HSMul.hSMul.{0, u1, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (instHSMul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoid.SMul.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Module.End.semiring.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
 Case conversion may be inaccurate. Consider using '#align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDerivₓ'. -/
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] :=
   by
@@ -274,7 +274,7 @@ theorem hasseDeriv_comp (k l : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_leₓ'. -/
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
   by
@@ -298,7 +298,7 @@ theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R Nat.hasZero (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDerivₓ'. -/
 theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
     natDegree (hasseDeriv n p) = natDegree p - n :=
@@ -324,7 +324,7 @@ open AddMonoidHom Finset.Nat
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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)) f g)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.Nat.antidiagonal k) (fun (ij : Prod.{0, 0} Nat Nat) => 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} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat ij)) f) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat ij)) g)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{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)) f g)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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)) f g)) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.Nat.antidiagonal k) (fun (ij : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) g) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat ij)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat ij)) g)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{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)) f g)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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)) f g)) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.Nat.antidiagonal k) (fun (ij : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) g) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat ij)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat ij)) g)))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mulₓ'. -/
 theorem hasseDeriv_mul (f g : R[X]) :
     hasseDeriv k (f * g) = ∑ ij in antidiagonal k, hasseDeriv ij.1 f * hasseDeriv ij.2 g :=

10bf4f82

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -175,7 +175,7 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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) 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_Cₓ'. -/
 theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,

10bf4f82

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -70,7 +70,7 @@ def hasseDeriv (k : ℕ) : R[X] →ₗ[R] R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) f (fun (i : Nat) (r : R) => coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) i k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Nat.choose i k)) r)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) f (fun (i : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose i k)) r)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) (Polynomial.sum.{u1, u1} R _inst_1 (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) f (fun (i : Nat) (r : R) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) i k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose i k)) r)))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_applyₓ'. -/
 theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (↑(i.choose k) * r) :=
   by simpa only [← nsmul_eq_mul]
@@ -80,7 +80,7 @@ theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) n) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k) k)) (Polynomial.coeff.{u1} R _inst_1 f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n k)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) n) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k) k)) (Polynomial.coeff.{u1} R _inst_1 f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) f) n) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k) k)) (Polynomial.coeff.{u1} R _inst_1 f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n k)))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeffₓ'. -/
 theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) :=
   by
@@ -102,7 +102,7 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) f) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) f) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) f) f
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_zero' Polynomial.hasseDeriv_zero'ₓ'. -/
 theorem hasseDeriv_zero' : hasseDeriv 0 f = f := by
   simp only [hasse_deriv_apply, tsub_zero, Nat.choose_zero_right, Nat.cast_one, one_mul,
@@ -120,7 +120,7 @@ theorem hasseDeriv_zero : @hasseDeriv R _ 0 = LinearMap.id :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) p) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_eq_zero_of_lt_nat_degree Polynomial.hasseDeriv_eq_zero_of_lt_natDegreeₓ'. -/
 theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree < n) :
     hasseDeriv n p = 0 := by
@@ -133,7 +133,7 @@ theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) f) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1) f)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_one' Polynomial.hasseDeriv_one'ₓ'. -/
 theorem hasseDeriv_one' : hasseDeriv 1 f = derivative f := by
   simp only [hasse_deriv_apply, derivative_apply, ← C_mul_X_pow_eq_monomial, Nat.choose_one_right,
@@ -151,7 +151,7 @@ theorem hasseDeriv_one : @hasseDeriv R _ 1 = derivative :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (n : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Nat.choose n k)) r))
 but is expected to have type
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Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose n k)) r))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (n : Nat) (r : R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) a) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R _inst_1) (Nat.choose n k)) r))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomialₓ'. -/
 @[simp]
 theorem hasseDeriv_monomial (n : ℕ) (r : R) :
@@ -175,7 +175,7 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_Cₓ'. -/
 theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
@@ -186,7 +186,7 @@ theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 1 (One.one.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.hasOne.{u1} R _inst_1))))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 1 (One.toOfNat1.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.one.{u1} R _inst_1)))) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply_one Polynomial.hasseDeriv_apply_oneₓ'. -/
 theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
   rw [← C_1, hasse_deriv_C k _ hk]
@@ -196,7 +196,7 @@ theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (Polynomial.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (Polynomial.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (Polynomial.zero.{u1} R _inst_1))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (Polynomial.X.{u1} R _inst_1)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (Polynomial.X.{u1} R _inst_1)) (Polynomial.zero.{u1} R _inst_1))))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_X Polynomial.hasseDeriv_Xₓ'. -/
 theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
@@ -207,7 +207,7 @@ theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), Eq.{succ u1} ((Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (SMul.smul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.hasSmul.{u1, u1, 0, u1, u1} R R Nat (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) Nat.monoid (Polynomial.distribMulAction.{u1, 0} R _inst_1 Nat Nat.monoid (Module.toDistribMulAction.{0, u1} Nat R Nat.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (AddCommMonoid.natModule.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Polynomial.smulCommClass.{u1, u1, 0} R _inst_1 R Nat (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Nat R Nat.hasZero (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddMonoid.natSMulWithZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (AddMonoid.nat_smulCommClass'.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), Eq.{succ u1} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HSMul.hSMul.{0, u1, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (instHSMul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoid.SMul.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Module.End.semiring.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), Eq.{succ u1} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HSMul.hSMul.{0, u1, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (instHSMul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoid.SMul.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Module.End.semiring.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
 Case conversion may be inaccurate. Consider using '#align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDerivₓ'. -/
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] :=
   by
@@ -274,7 +274,7 @@ theorem hasseDeriv_comp (k l : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_leₓ'. -/
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
   by
@@ -298,7 +298,7 @@ theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R Nat.hasZero (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDerivₓ'. -/
 theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
     natDegree (hasseDeriv n p) = natDegree p - n :=
@@ -324,7 +324,7 @@ open AddMonoidHom Finset.Nat
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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)) f g)) (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.Nat.antidiagonal k) (fun (ij : Prod.{0, 0} Nat Nat) => 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} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat ij)) f) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat ij)) g)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{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)) f g)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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)) f g)) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.Nat.antidiagonal k) (fun (ij : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) g) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat ij)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat ij)) g)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{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)) f g)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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)) f g)) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.Nat.antidiagonal k) (fun (ij : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) g) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ 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(Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat ij)) g)))
 Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mulₓ'. -/
 theorem hasseDeriv_mul (f g : R[X]) :
     hasseDeriv k (f * g) = ∑ ij in antidiagonal k, hasseDeriv ij.1 f * hasseDeriv ij.2 g :=

10bf4f82

bump to nightly-2023-05-10-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

27fff0df

Diff

@@ -205,7 +205,7 @@ theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
 
 /- warning: polynomial.factorial_smul_hasse_deriv -> Polynomial.factorial_smul_hasseDeriv is a dubious translation:
 lean 3 declaration is
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u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (SMul.smul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.hasSmul.{u1, u1, 0, u1, u1} R R Nat (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) Nat.monoid (Polynomial.distribMulAction.{u1, 0} R _inst_1 Nat Nat.monoid (Module.toDistribMulAction.{0, u1} Nat R Nat.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (AddCommMonoid.natModule.{u1} R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (Polynomial.smulCommClass.{u1, u1, 0} R _inst_1 R Nat (SMulWithZero.toSmulZeroClass.{u1, u1} R R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toSMulWithZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) (SMulWithZero.toSmulZeroClass.{0, u1} Nat R Nat.hasZero (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddMonoid.natSMulWithZero.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))) (AddMonoid.nat_smulCommClass'.{u1, u1} R R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u1} R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat), Eq.{succ u1} (forall (ᾰ : Polynomial.{u1} R _inst_1), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) ᾰ) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HSMul.hSMul.{0, u1, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (instHSMul.{0, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoid.SMul.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddMonoidWithOne.toAddMonoid.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Module.End.semiring.{u1, u1} R (Polynomial.{u1} R _inst_1) _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))))))))) (Nat.factorial k) (Polynomial.hasseDeriv.{u1} R _inst_1 k))) (Nat.iterate.{succ u1} (Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
 Case conversion may be inaccurate. Consider using '#align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDerivₓ'. -/

10bf4f82

bump to nightly-2023-03-16-03

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

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.polynomial.hasse_deriv
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Data.Polynomial.Derivative
 /-!
 # Hasse derivative of polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The `k`th Hasse derivative of a polynomial `∑ a_i X^i` is `∑ (i.choose k) a_i X^(i-k)`.
 It is a variant of the usual derivative, and satisfies `k! * (hasse_deriv k f) = derivative^[k] f`.
 The main benefit is that is gives an atomic way of talking about expressions such as

a148d797

bump to nightly-2023-03-13-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

a0c9db6f

Diff

@@ -55,16 +55,30 @@ open Nat hiding nsmul_eq_mul
 
 variable {R : Type _} [Semiring R] (k : ℕ) (f : R[X])
 
+#print Polynomial.hasseDeriv /-
 /-- The `k`th Hasse derivative of a polynomial `∑ a_i X^i` is `∑ (i.choose k) a_i X^(i-k)`.
 It satisfies `k! * (hasse_deriv k f) = derivative^[k] f`. -/
 def hasseDeriv (k : ℕ) : R[X] →ₗ[R] R[X] :=
   lsum fun i => monomial (i - k) ∘ₗ DistribMulAction.toLinearMap R R (i.choose k)
 #align polynomial.hasse_deriv Polynomial.hasseDeriv
+-/
 
+/- warning: polynomial.hasse_deriv_apply -> Polynomial.hasseDeriv_apply is a dubious translation:
+lean 3 declaration is
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(Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Nat.choose i k)) r)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_applyₓ'. -/
 theorem hasseDeriv_apply : hasseDeriv k f = f.Sum fun i r => monomial (i - k) (↑(i.choose k) * r) :=
   by simpa only [← nsmul_eq_mul]
 #align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_apply
 
+/- warning: polynomial.hasse_deriv_coeff -> Polynomial.hasseDeriv_coeff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeffₓ'. -/
 theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) :=
   by
   rw [hasse_deriv_apply, coeff_sum, sum_def, Finset.sum_eq_single (n + k), coeff_monomial]
@@ -81,16 +95,30 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
     simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
 #align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeff
 
+/- warning: polynomial.hasse_deriv_zero' -> Polynomial.hasseDeriv_zero' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_zero' Polynomial.hasseDeriv_zero'ₓ'. -/
 theorem hasseDeriv_zero' : hasseDeriv 0 f = f := by
   simp only [hasse_deriv_apply, tsub_zero, Nat.choose_zero_right, Nat.cast_one, one_mul,
     sum_monomial_eq]
 #align polynomial.hasse_deriv_zero' Polynomial.hasseDeriv_zero'
 
+#print Polynomial.hasseDeriv_zero /-
 @[simp]
 theorem hasseDeriv_zero : @hasseDeriv R _ 0 = LinearMap.id :=
   LinearMap.ext <| hasseDeriv_zero'
 #align polynomial.hasse_deriv_zero Polynomial.hasseDeriv_zero
+-/
 
+/- warning: polynomial.hasse_deriv_eq_zero_of_lt_nat_degree -> Polynomial.hasseDeriv_eq_zero_of_lt_natDegree is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (p : Polynomial.{u1} R _inst_1) (n : Nat), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 p) n) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_eq_zero_of_lt_nat_degree Polynomial.hasseDeriv_eq_zero_of_lt_natDegreeₓ'. -/
 theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree < n) :
     hasseDeriv n p = 0 := by
   rw [hasse_deriv_apply, sum_def]
@@ -98,16 +126,30 @@ theorem hasseDeriv_eq_zero_of_lt_natDegree (p : R[X]) (n : ℕ) (h : p.natDegree
   simp [Nat.choose_eq_zero_of_lt ((le_nat_degree_of_mem_supp _ hx).trans_lt h)]
 #align polynomial.hasse_deriv_eq_zero_of_lt_nat_degree Polynomial.hasseDeriv_eq_zero_of_lt_natDegree
 
+/- warning: polynomial.hasse_deriv_one' -> Polynomial.hasseDeriv_one' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_one' Polynomial.hasseDeriv_one'ₓ'. -/
 theorem hasseDeriv_one' : hasseDeriv 1 f = derivative f := by
   simp only [hasse_deriv_apply, derivative_apply, ← C_mul_X_pow_eq_monomial, Nat.choose_one_right,
     (Nat.cast_commute _ _).Eq]
 #align polynomial.hasse_deriv_one' Polynomial.hasseDeriv_one'
 
+#print Polynomial.hasseDeriv_one /-
 @[simp]
 theorem hasseDeriv_one : @hasseDeriv R _ 1 = derivative :=
   LinearMap.ext <| hasseDeriv_one'
 #align polynomial.hasse_deriv_one Polynomial.hasseDeriv_one
+-/
 
+/- warning: polynomial.hasse_deriv_monomial -> Polynomial.hasseDeriv_monomial is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomialₓ'. -/
 @[simp]
 theorem hasseDeriv_monomial (n : ℕ) (r : R) :
     hasseDeriv k (monomial n r) = monomial (n - k) (↑(n.choose k) * r) :=
@@ -126,20 +168,44 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
-theorem hasseDeriv_c (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
+/- warning: polynomial.hasse_deriv_C -> Polynomial.hasseDeriv_C is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) k) -> (Eq.{succ u1} (Polynomial.{u1} R _inst_1) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (r : R), (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) k) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (a : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) a) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_Cₓ'. -/
+theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     MulZeroClass.zero_mul, monomial_zero_right]
-#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_c
-
+#align polynomial.hasse_deriv_C Polynomial.hasseDeriv_C
+
+/- warning: polynomial.hasse_deriv_apply_one -> Polynomial.hasseDeriv_apply_one is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_apply_one Polynomial.hasseDeriv_apply_oneₓ'. -/
 theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
   rw [← C_1, hasse_deriv_C k _ hk]
 #align polynomial.hasse_deriv_apply_one Polynomial.hasseDeriv_apply_one
 
-theorem hasseDeriv_x (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
+/- warning: polynomial.hasse_deriv_X -> Polynomial.hasseDeriv_X is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_X Polynomial.hasseDeriv_Xₓ'. -/
+theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     MulZeroClass.zero_mul, monomial_zero_right]
-#align polynomial.hasse_deriv_X Polynomial.hasseDeriv_x
-
+#align polynomial.hasse_deriv_X Polynomial.hasseDeriv_X
+
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(Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.derivative.{u1} R _inst_1)) k)
+but is expected to have type
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_inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (HSMul.hSMul.{0, u1, u1} Nat (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) 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+Case conversion may be inaccurate. Consider using '#align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDerivₓ'. -/
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] :=
   by
   induction' k with k ih
@@ -168,6 +234,7 @@ theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative
   ring
 #align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDeriv
 
+#print Polynomial.hasseDeriv_comp /-
 theorem hasseDeriv_comp (k l : ℕ) :
     (@hasseDeriv R _ k).comp (hasseDeriv l) = (k + l).choose k • hasseDeriv (k + l) :=
   by
@@ -198,7 +265,14 @@ theorem hasseDeriv_comp (k l : ℕ) :
   · ring
   all_goals apply_rules [mul_ne_zero, H]
 #align polynomial.hasse_deriv_comp Polynomial.hasseDeriv_comp
+-/
 
+/- warning: polynomial.nat_degree_hasse_deriv_le -> Polynomial.natDegree_hasseDeriv_le is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_leₓ'. -/
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
   by
   classical
@@ -217,6 +291,12 @@ theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p
     · simp
 #align polynomial.nat_degree_hasse_deriv_le Polynomial.natDegree_hasseDeriv_le
 
+/- warning: polynomial.nat_degree_hasse_deriv -> Polynomial.natDegree_hasseDeriv is a dubious translation:
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R Nat.hasZero (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) n)
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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] [_inst_2 : NoZeroSMulDivisors.{0, u1} Nat R (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.SMul.{u1} R (AddMonoidWithOne.toAddMonoid.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))] (p : Polynomial.{u1} R _inst_1) (n : Nat), Eq.{1} Nat (Polynomial.natDegree.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 n) p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) n)
+Case conversion may be inaccurate. Consider using '#align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDerivₓ'. -/
 theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
     natDegree (hasseDeriv n p) = natDegree p - n :=
   by
@@ -237,6 +317,12 @@ section
 
 open AddMonoidHom Finset.Nat
 
+/- warning: polynomial.hasse_deriv_mul -> Polynomial.hasseDeriv_mul is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (k : Nat) (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{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)) f g)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 k) (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)) f g)) (Finset.sum.{u1, 0} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Prod.{0, 0} Nat Nat) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.Nat.antidiagonal k) (fun (ij : Prod.{0, 0} Nat Nat) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) g) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) f) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.fst.{0, 0} Nat Nat ij)) f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Polynomial.{u1} R _inst_1) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.hasseDeriv.{u1} R _inst_1 (Prod.snd.{0, 0} Nat Nat ij)) g)))
+Case conversion may be inaccurate. Consider using '#align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mulₓ'. -/
 theorem hasseDeriv_mul (f g : R[X]) :
     hasseDeriv k (f * g) = ∑ ij in antidiagonal k, hasseDeriv ij.1 f * hasseDeriv ij.2 g :=
   by

a148d797

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -72,13 +72,13 @@ theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k
   · intro i hi hink
     rw [coeff_monomial]
     by_cases hik : i < k
-    · simp only [Nat.choose_eq_zero_of_lt hik, if_t_t, Nat.cast_zero, zero_mul]
+    · simp only [Nat.choose_eq_zero_of_lt hik, if_t_t, Nat.cast_zero, MulZeroClass.zero_mul]
     · push_neg  at hik
       rw [if_neg]
       contrapose! hink
       exact (tsub_eq_iff_eq_add_of_le hik).mp hink
   · intro h
-    simp only [not_mem_support_iff.mp h, monomial_zero_right, mul_zero, coeff_zero]
+    simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
 #align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeff
 
 theorem hasseDeriv_zero' : hasseDeriv 0 f = f := by
@@ -118,17 +118,17 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
   · rw [if_pos hnik, if_pos, ← hnik]
     apply tsub_eq_of_eq_add_rev
     rwa [add_comm]
-  · rw [if_neg hnik, mul_zero]
+  · rw [if_neg hnik, MulZeroClass.mul_zero]
     by_cases hkn : k ≤ n
     · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik
       rw [if_neg hnik]
     · push_neg  at hkn
-      rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, zero_mul, if_t_t]
+      rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
 theorem hasseDeriv_c (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
-    zero_mul, monomial_zero_right]
+    MulZeroClass.zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_C Polynomial.hasseDeriv_c
 
 theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
@@ -137,7 +137,7 @@ theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
 
 theorem hasseDeriv_x (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
-    zero_mul, monomial_zero_right]
+    MulZeroClass.zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_X Polynomial.hasseDeriv_x
 
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] :=
@@ -173,17 +173,17 @@ theorem hasseDeriv_comp (k l : ℕ) :
   by
   ext i : 2
   simp only [LinearMap.smul_apply, comp_app, LinearMap.coe_comp, smul_monomial, hasse_deriv_apply,
-    mul_one, monomial_eq_zero_iff, sum_monomial_index, mul_zero, ← tsub_add_eq_tsub_tsub,
-    add_comm l k]
+    mul_one, monomial_eq_zero_iff, sum_monomial_index, MulZeroClass.mul_zero, ←
+    tsub_add_eq_tsub_tsub, add_comm l k]
   rw_mod_cast [nsmul_eq_mul]
   congr 2
   by_cases hikl : i < k + l
-  · rw [choose_eq_zero_of_lt hikl, mul_zero]
+  · rw [choose_eq_zero_of_lt hikl, MulZeroClass.mul_zero]
     by_cases hil : i < l
-    · rw [choose_eq_zero_of_lt hil, mul_zero]
+    · rw [choose_eq_zero_of_lt hil, MulZeroClass.mul_zero]
     · push_neg  at hil
       rw [← tsub_lt_iff_right hil] at hikl
-      rw [choose_eq_zero_of_lt hikl, zero_mul]
+      rw [choose_eq_zero_of_lt hikl, MulZeroClass.zero_mul]
   push_neg  at hikl
   apply @cast_injective ℚ
   have h1 : l ≤ i := le_of_add_le_right hikl
@@ -261,11 +261,13 @@ theorem hasseDeriv_mul (f g : R[X]) :
     rw [Finset.Nat.mem_antidiagonal] at hx
     subst hx
     by_cases hm : m < x.1
-    · simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, zero_mul, monomial_zero_right]
-    by_cases hn : n < x.2
     ·
-      simp only [Nat.choose_eq_zero_of_lt hn, Nat.cast_zero, zero_mul, mul_zero,
+      simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, MulZeroClass.zero_mul,
         monomial_zero_right]
+    by_cases hn : n < x.2
+    ·
+      simp only [Nat.choose_eq_zero_of_lt hn, Nat.cast_zero, MulZeroClass.zero_mul,
+        MulZeroClass.mul_zero, monomial_zero_right]
     push_neg  at hm hn
     rw [tsub_add_eq_add_tsub hm, ← add_tsub_assoc_of_le hn, ← tsub_add_eq_tsub_tsub,
       add_comm x.2 x.1, mul_assoc, ← mul_assoc r, ← (Nat.cast_commute _ r).Eq, mul_assoc, mul_assoc]

a148d797

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -126,7 +126,7 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, zero_mul, if_t_t]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
-theorem hasseDeriv_c (r : R) (hk : 0 < k) : hasseDeriv k (c r) = 0 := by
+theorem hasseDeriv_c (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_C Polynomial.hasseDeriv_c
@@ -135,7 +135,7 @@ theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
   rw [← C_1, hasse_deriv_C k _ hk]
 #align polynomial.hasse_deriv_apply_one Polynomial.hasseDeriv_apply_one
 
-theorem hasseDeriv_x (hk : 1 < k) : hasseDeriv k (x : R[X]) = 0 := by
+theorem hasseDeriv_x (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasse_deriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
     zero_mul, monomial_zero_right]
 #align polynomial.hasse_deriv_X Polynomial.hasseDeriv_x

a148d797

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

a148d797

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

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

56e439ec

Diff

@@ -4,9 +4,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
 import Mathlib.Algebra.Polynomial.BigOperators
+import Mathlib.Algebra.Polynomial.Derivative
 import Mathlib.Data.Nat.Choose.Cast
 import Mathlib.Data.Nat.Choose.Vandermonde
-import Mathlib.Data.Polynomial.Derivative
 import Mathlib.Tactic.FieldSimp
 
 #align_import data.polynomial.hasse_deriv from "leanprover-community/mathlib"@"a148d797a1094ab554ad4183a4ad6f130358ef64"

a148d797

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -199,7 +199,7 @@ theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) :
     simp_rw [Function.comp, natDegree_monomial]
     rw [Finset.fold_ite, Finset.fold_const]
     · simp only [ite_self, max_eq_right, zero_le', Finset.fold_max_le, true_and_iff, and_imp,
-        tsub_le_iff_right, mem_support_iff, Ne.def, Finset.mem_filter]
+        tsub_le_iff_right, mem_support_iff, Ne, Finset.mem_filter]
       intro x hx hx'
       have hxp : x ≤ p.natDegree := le_natDegree_of_ne_zero hx
       have hxn : n ≤ x := by
@@ -216,7 +216,7 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
   · refine' map_natDegree_eq_sub _ _
     · exact fun h => hasseDeriv_eq_zero_of_lt_natDegree _ _
     · classical
-        simp only [ite_eq_right_iff, Ne.def, natDegree_monomial, hasseDeriv_monomial]
+        simp only [ite_eq_right_iff, Ne, natDegree_monomial, hasseDeriv_monomial]
         intro k c c0 hh
         -- this is where we use the `smul_eq_zero` from `NoZeroSMulDivisors`
         rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh

a148d797

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -240,7 +240,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
   congr 2
   clear f g
   ext m r n s : 4
-  simp only [finset_sum_apply, coe_mulLeft, coe_comp, flip_apply, Function.comp_apply,
+  simp only [Φ, D, finset_sum_apply, coe_mulLeft, coe_comp, flip_apply, Function.comp_apply,
              hasseDeriv_monomial, LinearMap.toAddMonoidHom_coe, compHom_apply_apply,
              coe_mul, monomial_mul_monomial]
   have aux :

a148d797

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -158,7 +158,7 @@ theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = (@derivativ
   rw [mul_comm (k+1) _, mul_assoc, mul_assoc]
   congr 1
   have : n + k + 1 = n + (k + 1) := by apply add_assoc
-  rw [←choose_symm_of_eq_add this, choose_succ_right_eq, mul_comm]
+  rw [← choose_symm_of_eq_add this, choose_succ_right_eq, mul_comm]
   congr
   rw [add_assoc, add_tsub_cancel_left]
 #align polynomial.factorial_smul_hasse_deriv Polynomial.factorial_smul_hasseDeriv
@@ -170,7 +170,7 @@ theorem hasseDeriv_comp (k l : ℕ) :
     mul_one, monomial_eq_zero_iff, sum_monomial_index, mul_zero, ←
     tsub_add_eq_tsub_tsub, add_comm l k]
   rw_mod_cast [nsmul_eq_mul]
-  rw [←Nat.cast_mul]
+  rw [← Nat.cast_mul]
   congr 2
   by_cases hikl : i < k + l
   · rw [choose_eq_zero_of_lt hikl, mul_zero]
@@ -263,7 +263,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
   rw [Finset.sum_congr rfl aux]
   rw [← map_sum, ← Finset.sum_mul]
   congr
-  rw_mod_cast [←Nat.add_choose_eq]
+  rw_mod_cast [← Nat.add_choose_eq]
 #align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mul
 
 end

a148d797

feat(Data.Finset.Antidiagonal): generalize Finset.Nat.antidiagonal (#7486)

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

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

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

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

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

TODO

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

This closes #7917

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

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

85a1f28f

Diff

@@ -227,6 +227,8 @@ section
 
 open AddMonoidHom Finset.Nat
 
+open Finset (antidiagonal mem_antidiagonal)
+
 theorem hasseDeriv_mul (f g : R[X]) :
     hasseDeriv k (f * g) = ∑ ij in antidiagonal k, hasseDeriv ij.1 f * hasseDeriv ij.2 g := by
   let D k := (@hasseDeriv R _ k).toAddMonoidHom
@@ -247,7 +249,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
         monomial (m - x.1 + (n - x.2)) (↑(m.choose x.1) * r * (↑(n.choose x.2) * s)) =
           monomial (m + n - k) (↑(m.choose x.1) * ↑(n.choose x.2) * (r * s)) := by
     intro x hx
-    rw [Finset.Nat.mem_antidiagonal] at hx
+    rw [mem_antidiagonal] at hx
     subst hx
     by_cases hm : m < x.1
     · simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, zero_mul,

a148d797

chore: use _root_.map_sum more consistently (#7189)

Also _root_.map_smul when in the neighbourhood.

1fa13fb0

Diff

@@ -259,7 +259,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     rw [tsub_add_eq_add_tsub hm, ← add_tsub_assoc_of_le hn, ← tsub_add_eq_tsub_tsub,
       add_comm x.2 x.1, mul_assoc, ← mul_assoc r, ← (Nat.cast_commute _ r).eq, mul_assoc, mul_assoc]
   rw [Finset.sum_congr rfl aux]
-  rw [← LinearMap.map_sum, ← Finset.sum_mul]
+  rw [← map_sum, ← Finset.sum_mul]
   congr
   rw_mod_cast [←Nat.add_choose_eq]
 #align polynomial.hasse_deriv_mul Polynomial.hasseDeriv_mul

a148d797

field_simp: Use positivity as a discharger (#6312)

The main reasons is that having h : 0 < denom in the context should suffice for field_simp to do its job, without the need to manually pass h.ne or similar.

Quite a few have := … ≠ 0 could be dropped, and some field_simp calls no longer need explicit arguments; this is promising.

This does break some proofs where field_simp was not used as a closing tactic, and it now shuffles terms around a bit different. These were fixed. Using field_simp in the middle of a proof seems rather fragile anyways.

As a drive-by contribution, positivity now knows about π > 0.

fixes: #4835

Co-authored-by: Matthew Ballard <matt@mrb.email>

6b391efa

Diff

@@ -188,9 +188,7 @@ theorem hasseDeriv_comp (k l : ℕ) :
   rw [cast_choose ℚ h1, cast_choose ℚ h2, cast_choose ℚ h3, cast_choose ℚ hikl]
   rw [show i - (k + l) = i - l - k by rw [add_comm]; apply tsub_add_eq_tsub_tsub]
   simp only [add_tsub_cancel_left]
-  have H : ∀ n : ℕ, (n ! : ℚ) ≠ 0 := by exact_mod_cast factorial_ne_zero
-  field_simp [H]
-  ring
+  field_simp; ring
 #align polynomial.hasse_deriv_comp Polynomial.hasseDeriv_comp
 
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) :

a148d797

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

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).

277dea95

Diff

@@ -73,13 +73,13 @@ theorem hasseDeriv_coeff (n : ℕ) :
   · intro i _hi hink
     rw [coeff_monomial]
     by_cases hik : i < k
-    · simp only [Nat.choose_eq_zero_of_lt hik, ite_self, Nat.cast_zero, MulZeroClass.zero_mul]
+    · simp only [Nat.choose_eq_zero_of_lt hik, ite_self, Nat.cast_zero, zero_mul]
     · push_neg at hik
       rw [if_neg]
       contrapose! hink
       exact (tsub_eq_iff_eq_add_of_le hik).mp hink
   · intro h
-    simp only [not_mem_support_iff.mp h, monomial_zero_right, MulZeroClass.mul_zero, coeff_zero]
+    simp only [not_mem_support_iff.mp h, monomial_zero_right, mul_zero, coeff_zero]
 #align polynomial.hasse_deriv_coeff Polynomial.hasseDeriv_coeff
 
 theorem hasseDeriv_zero' : hasseDeriv 0 f = f := by
@@ -118,17 +118,17 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
   · rw [if_pos hnik, if_pos, ← hnik]
     apply tsub_eq_of_eq_add_rev
     rwa [add_comm]
-  · rw [if_neg hnik, MulZeroClass.mul_zero]
+  · rw [if_neg hnik, mul_zero]
     by_cases hkn : k ≤ n
     · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik
       rw [if_neg hnik]
     · push_neg at hkn
-      rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, ite_self]
+      rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, zero_mul, ite_self]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial
 
 theorem hasseDeriv_C (r : R) (hk : 0 < k) : hasseDeriv k (C r) = 0 := by
   rw [← monomial_zero_left, hasseDeriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
-    MulZeroClass.zero_mul, monomial_zero_right]
+    zero_mul, monomial_zero_right]
 set_option linter.uppercaseLean3 false in
 #align polynomial.hasse_deriv_C Polynomial.hasseDeriv_C
 
@@ -138,7 +138,7 @@ theorem hasseDeriv_apply_one (hk : 0 < k) : hasseDeriv k (1 : R[X]) = 0 := by
 
 theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
   rw [← monomial_one_one_eq_X, hasseDeriv_monomial, Nat.choose_eq_zero_of_lt hk, Nat.cast_zero,
-    MulZeroClass.zero_mul, monomial_zero_right]
+    zero_mul, monomial_zero_right]
 set_option linter.uppercaseLean3 false in
 #align polynomial.hasse_deriv_X Polynomial.hasseDeriv_X
 
@@ -252,11 +252,11 @@ theorem hasseDeriv_mul (f g : R[X]) :
     rw [Finset.Nat.mem_antidiagonal] at hx
     subst hx
     by_cases hm : m < x.1
-    · simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, MulZeroClass.zero_mul,
+    · simp only [Nat.choose_eq_zero_of_lt hm, Nat.cast_zero, zero_mul,
                  monomial_zero_right]
     by_cases hn : n < x.2
-    · simp only [Nat.choose_eq_zero_of_lt hn, Nat.cast_zero, MulZeroClass.zero_mul,
-                 MulZeroClass.mul_zero, monomial_zero_right]
+    · simp only [Nat.choose_eq_zero_of_lt hn, Nat.cast_zero, zero_mul,
+                 mul_zero, monomial_zero_right]
     push_neg at hm hn
     rw [tsub_add_eq_add_tsub hm, ← add_tsub_assoc_of_le hn, ← tsub_add_eq_tsub_tsub,
       add_comm x.2 x.1, mul_assoc, ← mul_assoc r, ← (Nat.cast_commute _ r).eq, mul_assoc, mul_assoc]

a148d797

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -51,7 +51,7 @@ open Function
 
 open Nat hiding nsmul_eq_mul
 
-variable {R : Type _} [Semiring R] (k : ℕ) (f : R[X])
+variable {R : Type*} [Semiring R] (k : ℕ) (f : R[X])
 
 /-- The `k`th Hasse derivative of a polynomial `∑ a_i X^i` is `∑ (i.choose k) a_i X^(i-k)`.
 It satisfies `k! * (hasse_deriv k f) = derivative^[k] f`. -/

a148d797

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.polynomial.hasse_deriv
-! leanprover-community/mathlib commit a148d797a1094ab554ad4183a4ad6f130358ef64
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Polynomial.BigOperators
 import Mathlib.Data.Nat.Choose.Cast
@@ -14,6 +9,8 @@ import Mathlib.Data.Nat.Choose.Vandermonde
 import Mathlib.Data.Polynomial.Derivative
 import Mathlib.Tactic.FieldSimp
 
+#align_import data.polynomial.hasse_deriv from "leanprover-community/mathlib"@"a148d797a1094ab554ad4183a4ad6f130358ef64"
+
 /-!
 # Hasse derivative of polynomials

a148d797

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -145,7 +145,7 @@ theorem hasseDeriv_X (hk : 1 < k) : hasseDeriv k (X : R[X]) = 0 := by
 set_option linter.uppercaseLean3 false in
 #align polynomial.hasse_deriv_X Polynomial.hasseDeriv_X
 
-theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] := by
+theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = (@derivative R _)^[k] := by
   induction' k with k ih
   · rw [hasseDeriv_zero, factorial_zero, iterate_zero, one_smul, LinearMap.id_coe]
   ext f n : 2

a148d797

chore: clean up spacing around at and goals (#5387)

Changes are of the form

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

2a870323

Diff

@@ -125,7 +125,7 @@ theorem hasseDeriv_monomial (n : ℕ) (r : R) :
     by_cases hkn : k ≤ n
     · rw [← tsub_eq_iff_eq_add_of_le hkn] at hnik
       rw [if_neg hnik]
-    · push_neg  at hkn
+    · push_neg at hkn
       rw [Nat.choose_eq_zero_of_lt hkn, Nat.cast_zero, MulZeroClass.zero_mul, ite_self]
 #align polynomial.hasse_deriv_monomial Polynomial.hasseDeriv_monomial

a148d797

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -148,7 +148,7 @@ set_option linter.uppercaseLean3 false in
 theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative R _^[k] := by
   induction' k with k ih
   · rw [hasseDeriv_zero, factorial_zero, iterate_zero, one_smul, LinearMap.id_coe]
-  ext (f n) : 2
+  ext f n : 2
   rw [iterate_succ_apply', ← ih]
   simp only [LinearMap.smul_apply, coeff_smul, LinearMap.map_smul_of_tower, coeff_derivative,
     hasseDeriv_coeff, ← @choose_symm_add _ k]
@@ -242,7 +242,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
   simp only [← finset_sum_apply]
   congr 2
   clear f g
-  ext (m r n s) : 4
+  ext m r n s : 4
   simp only [finset_sum_apply, coe_mulLeft, coe_comp, flip_apply, Function.comp_apply,
              hasseDeriv_monomial, LinearMap.toAddMonoidHom_coe, compHom_apply_apply,
              coe_mul, monomial_mul_monomial]

a148d797

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

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

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

14167e48

Diff

@@ -69,8 +69,8 @@ theorem hasseDeriv_apply :
   apply nsmul_eq_mul
 #align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_apply
 
-theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) :=
-  by
+theorem hasseDeriv_coeff (n : ℕ) :
+    (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) := by
   rw [hasseDeriv_apply, coeff_sum, sum_def, Finset.sum_eq_single (n + k), coeff_monomial]
   · simp only [if_true, add_tsub_cancel_right, eq_self_iff_true]
   · intro i _hi hink
@@ -196,8 +196,8 @@ theorem hasseDeriv_comp (k l : ℕ) :
   ring
 #align polynomial.hasse_deriv_comp Polynomial.hasseDeriv_comp
 
-theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=
-  by
+theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) :
+    natDegree (hasseDeriv n p) ≤ natDegree p - n := by
   classical
     rw [hasseDeriv_apply, sum_def]
     refine' (natDegree_sum_le _ _).trans _
@@ -250,8 +250,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
     ∀ x : ℕ × ℕ,
       x ∈ antidiagonal k →
         monomial (m - x.1 + (n - x.2)) (↑(m.choose x.1) * r * (↑(n.choose x.2) * s)) =
-          monomial (m + n - k) (↑(m.choose x.1) * ↑(n.choose x.2) * (r * s)) :=
-    by
+          monomial (m + n - k) (↑(m.choose x.1) * ↑(n.choose x.2) * (r * s)) := by
     intro x hx
     rw [Finset.Nat.mem_antidiagonal] at hx
     subst hx

a148d797

chore: tidy various files (#3124)

55209140

Diff

@@ -243,7 +243,7 @@ theorem hasseDeriv_mul (f g : R[X]) :
   congr 2
   clear f g
   ext (m r n s) : 4
-  simp only [finset_sum_apply, coe_mul_left, coe_comp, flip_apply, Function.comp_apply,
+  simp only [finset_sum_apply, coe_mulLeft, coe_comp, flip_apply, Function.comp_apply,
              hasseDeriv_monomial, LinearMap.toAddMonoidHom_coe, compHom_apply_apply,
              coe_mul, monomial_mul_monomial]
   have aux :

a148d797

chore: tidy various files (#2950)

f03c405e

Diff

@@ -62,10 +62,11 @@ def hasseDeriv (k : ℕ) : R[X] →ₗ[R] R[X] :=
   lsum fun i => monomial (i - k) ∘ₗ DistribMulAction.toLinearMap R R (i.choose k)
 #align polynomial.hasse_deriv Polynomial.hasseDeriv
 
-theorem hasseDeriv_apply : hasseDeriv k f = f.sum fun i r => monomial (i - k) (↑(i.choose k) * r) :=
-  by dsimp [hasseDeriv]
-     congr; ext; congr
-     apply nsmul_eq_mul
+theorem hasseDeriv_apply :
+    hasseDeriv k f = f.sum fun i r => monomial (i - k) (↑(i.choose k) * r) := by
+  dsimp [hasseDeriv]
+  congr; ext; congr
+  apply nsmul_eq_mul
 #align polynomial.hasse_deriv_apply Polynomial.hasseDeriv_apply
 
 theorem hasseDeriv_coeff (n : ℕ) : (hasseDeriv k f).coeff n = (n + k).choose k * f.coeff (n + k) :=
@@ -219,11 +220,10 @@ theorem natDegree_hasseDeriv [NoZeroSMulDivisors ℕ R] (p : R[X]) (n : ℕ) :
   · simpa [hasseDeriv_eq_zero_of_lt_natDegree, hn] using (tsub_eq_zero_of_le hn.le).symm
   · refine' map_natDegree_eq_sub _ _
     · exact fun h => hasseDeriv_eq_zero_of_lt_natDegree _ _
-    ·
-      classical
+    · classical
         simp only [ite_eq_right_iff, Ne.def, natDegree_monomial, hasseDeriv_monomial]
         intro k c c0 hh
-        -- this is where we use the `smul_eq_zero` from `no_zero_smul_divisors`
+        -- this is where we use the `smul_eq_zero` from `NoZeroSMulDivisors`
         rw [← nsmul_eq_mul, smul_eq_zero, Nat.choose_eq_zero_iff] at hh
         exact (tsub_eq_zero_of_le (Or.resolve_right hh c0).le).symm
 #align polynomial.nat_degree_hasse_deriv Polynomial.natDegree_hasseDeriv

a148d797

fix: Re-enable two extensionality lemmas (#2859)

This fix was found when working on #2850.

A proof in HasseDeriv is fixed to deal with the change in ext behavior, by undoing some of the changes made when porting.

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

c341176c

Diff

@@ -167,47 +167,32 @@ theorem factorial_smul_hasseDeriv : ⇑(k ! • @hasseDeriv R _ k) = @derivative
 
 theorem hasseDeriv_comp (k l : ℕ) :
     (@hasseDeriv R _ k).comp (hasseDeriv l) = (k + l).choose k • hasseDeriv (k + l) := by
-  ext i x n
+  ext i : 2
   simp only [LinearMap.smul_apply, comp_apply, LinearMap.coe_comp, smul_monomial, hasseDeriv_apply,
-    mul_one, monomial_eq_zero_iff, sum_monomial_index, MulZeroClass.mul_zero, ←
+    mul_one, monomial_eq_zero_iff, sum_monomial_index, mul_zero, ←
     tsub_add_eq_tsub_tsub, add_comm l k]
   rw_mod_cast [nsmul_eq_mul]
-  congr 1
-  congr 1
+  rw [←Nat.cast_mul]
+  congr 2
   by_cases hikl : i < k + l
-  · rw [choose_eq_zero_of_lt hikl]
+  · rw [choose_eq_zero_of_lt hikl, mul_zero]
     by_cases hil : i < l
-    · rw [choose_eq_zero_of_lt hil]
-      simp
+    · rw [choose_eq_zero_of_lt hil, mul_zero]
     · push_neg at hil
       rw [← tsub_lt_iff_right hil] at hikl
-      rw [choose_eq_zero_of_lt hikl]
-      simp
+      rw [choose_eq_zero_of_lt hikl, zero_mul]
   push_neg at hikl
-  rw [←mul_assoc]
-  rw [←mul_assoc]
-  congr 1
-  norm_cast
-  congr 1
+  apply @cast_injective ℚ
   have h1 : l ≤ i := le_of_add_le_right hikl
   have h2 : k ≤ i - l := le_tsub_of_add_le_right hikl
   have h3 : k ≤ k + l := le_self_add
-  apply @cast_injective ℚ
   push_cast
-  rw [cast_choose ℚ h1]
-  rw [cast_choose ℚ h2]
-  rw [cast_choose ℚ h3]
-  rw [cast_choose ℚ hikl]
+  rw [cast_choose ℚ h1, cast_choose ℚ h2, cast_choose ℚ h3, cast_choose ℚ hikl]
   rw [show i - (k + l) = i - l - k by rw [add_comm]; apply tsub_add_eq_tsub_tsub]
   simp only [add_tsub_cancel_left]
   have H : ∀ n : ℕ, (n ! : ℚ) ≠ 0 := by exact_mod_cast factorial_ne_zero
-  have := H (i - l)
-  have := H k
-  have := H (i - l - k)
-  have := H l
-  have := H (k + l)
-  field_simp
-  ring_nf
+  field_simp [H]
+  ring
 #align polynomial.hasse_deriv_comp Polynomial.hasseDeriv_comp
 
 theorem natDegree_hasseDeriv_le (p : R[X]) (n : ℕ) : natDegree (hasseDeriv n p) ≤ natDegree p - n :=

a148d797

feat: Port Data.Polynomial.HasseDeriv (#2842)

ac9d2970

`data.polynomial.hasse_deriv` ⟷ `Mathlib.Data.Polynomial.HasseDeriv`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

TODO

Dependencies 8 + 416

data.polynomial.hasse_deriv ⟷ Mathlib.Data.Polynomial.HasseDeriv

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

TODO

Dependencies 8 + 416

`data.polynomial.hasse_deriv` ⟷ `Mathlib.Data.Polynomial.HasseDeriv`